The hydrogen line at 656.46 nm shifts to about 655.80 nm if a star is traveling 300 km/s toward Earth.
Using the Doppler Effect to Determine the Wavelength Shift
First, note the speed of light: c = 299,792 km/s.Original wavelength of the hydrogen line: λ₀ = 656.46 nm.Star's velocity towards Earth: v = -300 km/s (negative because the star is approaching).Use the Doppler shift formula for wavelengths:
[tex]\[\lambda = \lambda_0 \sqrt{\frac{c - v}{c + v}}\][/tex]Plugging in the values:
[tex]\[\lambda = 656.46 \, \text{nm} \sqrt{\frac{299,792 - 300}{299,792 + 300}}\][/tex]Calculate the ratio:
Ratio = √(299,492 / 300,092) ≈ √(0.998)Evaluate the square root:
[tex]\[\frac{299,492}{300,092} \approx 0.998\][/tex][tex]\[\sqrt{0.998} \approx 0.999\][/tex]Compute the shifted wavelength:
[tex]\[\lambda \approx 656.46 \, \text{nm} \times 0.999\][/tex] ≈ 655.80 nmThe 656.46-nm line would shift to approximately 655.80 nm if the star were moving towards Earth at 300 km/s.
Complete question:
Suppose that you'd like to find out if a distant star is moving relative to the earth. The star is much too far away to detect any change in its brightness as it moves toward or away from the earth. Instead we can use the Doppler effect to determine its relative speed. For this problem we are going to look at the spectral lines from hydrogen, specifically the one with a wavelength of 656.46 nm. Even at such low fractions of the speed of light these stars are moving quite quickly (thousands of kilometers a second) compared to the standard velocity dispersion in the Milky Way galaxy (which is around 300 km/s). Suppose the star was actually moving toward the earth at a more reasonable 300 km/s. What wavelength I would the 656.46-nm line move to? Use 299, 792 km/s for the speed of light. Express your answer in nanometers to five significant figures.
When violet light of wavelength 415 nm falls on a single slit, it creates a central diffraction peak that is 9.90 cm wide on a screen that is 2.53 m away. how wide is the slit?
Final answer:
The width of the slit when violet light of 415 nm wavelength creates a central diffraction peak of 9.90 cm on a screen 2.53 m away is approximately 10.6 μm.
Explanation:
The wavelength of violet light is given as 415 nm, and it produces a diffraction pattern with a central peak width of 9.90 cm on a screen 2.53 meters away. We can find the width of the slit using the formula for single-slit diffraction:
Δy = λL/a
where Δy is the width of the central peak, λ is the wavelength, L is the distance to the screen, and a is the width of the slit. Rearranging the formula to solve for a, we have:
a = λL/Δy
Substituting the provided values:
a = (415 x 10^-9 m)(2.53 m) / (9.90 x 10^-2 m)
After calculating, we find that the width of the slit (a) is approximately:
a ≈ 1.06 x 10^-5 m or 10.6 μm
Using the single-slit diffraction formula and given values, we calculate the width of the slit to be 21.1 μm.
To solve this problem, we'll use the formula for the width of the central peak in a single-slit diffraction pattern:
w = 2Lλ / aWhere:
w = width of the central peak (9.90 cm = 0.099 m)L = distance from the slit to the screen (2.53 m)λ = wavelength of violet light (415 nm = 415 x 10⁻⁹ m)a = width of the slit (what we need to find)Rearranging the formula to solve for a:
a = 2Lλ / wSubstituting the given values:
a = (2 * 2.53 m * 415 x 10⁻⁹ m) / 0.099 mNow, calculate:
a = 2.11 x 10⁻⁵ m or 21.1 μmTherefore, the width of the slit is 21.1 μm.
Picturing the way a volcano erupts to remember how a volcano functions is called a. Visualizing c. Keywording b. Categorizing d. All of these
Making a mental picture of the way a volcano erupts to remember how a volcano functions is called visualization.
What is visualization?Visualization is the process whereby a person makes or forms a mental picture of a particular situation or occurrence in order to better understand that occurrence.
Picturing the way a volcano erupts to remember how a volcano functions is a process of visualization.
A mental picture of the volcano is made by the individual.
Therefore, Picturing the way a volcano erupts to remember how a volcano functions is called visualization.
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A light source emits a beam of photons, each of which has a momentum of 2.7 × 10-29 kg·m/s. (a) what is the frequency of the photons? (b) to what region of the electromagnetic spectrum do the photons belong?
The frequency of the photons is equal to 1.22 ×10¹³ Hz and lies in the infrared region of the electromagnetic spectrum.
What is the frequency?The frequency of the photons or light can be described as the number of oscillations in one second. The frequency possesses S.I. units per second or Hertz.
The relationship between momentum (p), frequency (ν), and speed of light (c) is:
p = hν/c
ν = pc/h
Given, the momentum of the photons, p = 2.7 ×10⁻²⁹ Kg.m/s
The speed of light, c = 3×10⁸ m/s
The plank's constant, h = 6.626 ×10⁻³⁴ Js
The frequency of the photons can determine from the above-mentioned relationship:
ν = (2.7 × 10⁻²⁹).( 3 × 10⁸)/ 6.626 × 10⁻³⁴
ν = 1.22 × 10¹³ Hz
Therefore, the frequency of the photons is 1.22 × 10¹³ Hz and lies in the infrared region of the spectrum.
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Marie notices that most of her friends have MP3 players that are all made by a certain brand. She wants one, too, but not just any MP3 player. Marie wants to buy the exact same brand that her friends have. She thinks this is the way to fit in. Which term describes why Marie only wants a certain brand of MP3 player
What potential increase vac must an electron be accelerated through if the most energetic photon it can emit will scatter off of a stationary electron at an angle ϕ=60∘ with wavelength 8.4×10−12m?express your answer in kilovolts to two significant digits?
The pressure exerted by a phonograph needle on a record is surprisingly large. if the equivalent of 1.00 g is supported by a needle, the tip of which is a circle 0.210 mm in radius, what pressure is exerted on the record in n/m2?
The pressure exerted by a phonograph needle on a record, if the equivalent of 1g is supported by the needle with a radius of 0.210 mm, is approximately 7.05*10^7 Pa or N/m².
Explanation:
The pressure exerted by a phonograph needle on a record is calculated using the formula for pressure: P = F / A . To obtain the force (F), we multiply the mass of the needle (1g or 0.001 kg) by the acceleration due to gravity (9.8 m/s²). This yields a force of 0.0098 N. The area (A) is calculated using the formula for the area of a circle, A=πr², where r is the radius of the needle tip (0.210 mm or 0.00021 m). So, the area amounts to roughly 0.000000139 m². The resulting pressure (P), when calculated comes out to be approximately 7.05*10^7 Pa or N/m².
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A steam turbine operates at a boiler temperature of 450 k and an exhaust temperature of 300 k. what is the maximum theoretical efficiency of this system?
The maximum theoretical efficiency of a steam turbine operating at a boiler temperature of 450 K and an exhaust temperature of 300 K, as calculated by the Carnot efficiency, is approximately 33%.
Explanation:The efficiency of a heat engine like a steam turbine can be evaluated using the Carnot efficiency formula. The Carnot efficiency formula is 1 - Tc/Th where Tc is the cold reservoir temperature (exhaust temperature) and Th is the hot reservoir temperature (boiler temperature). Given in the problem, Tc=300K and Th=450K:
Efficiency = 1 - Tc/Th
= 1 - 300 K / 450 K = 1 - 0.67 approximately
So, the maximum theoretical efficiency of the steam turbine would be about 33% according to the Carnot efficiency.
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A 10 µf capacitor is charged to 108 v and is then connected across a 328 ω resistor. what is the initial charge on the capacitor? answer in units of µc.
A ball is thrown vertically upward with a speed of 1.53 m/s from a point 4.21 m above the ground. calculate the time in which the ball will reach the ground.
The time in which the ball will reach the ground is about 1.10 s
Further explanationAcceleration is rate of change of velocity.
[tex]\large {\boxed {a = \frac{v - u}{t} } }[/tex]
[tex]\large {\boxed {d = \frac{v + u}{2}~t } }[/tex]
a = acceleration ( m/s² )
v = final velocity ( m/s )
u = initial velocity ( m/s )
t = time taken ( s )
d = distance ( m )
Let us now tackle the problem !
This problem is about Kinematics.
We will solve it in the following way
Given:
initial speed = u = 1.53 m/s
initial height = H = 4.21 m
Unknown:
time taken = t = ?
Solution:
[tex]H = ut - \frac{1}{2}gt^2[/tex]
[tex]-4.21 = 1.53t - \frac{1}{2}(9.8)t^2[/tex]
[tex]-4.21 = 1.53t - 4.9t^2[/tex]
[tex]4.9t^2 - 1.53t - 4.21 = 0[/tex]
We will solve the above equation using the following quadratic function formula:
[tex]t = \frac{1.53 + \sqrt{1.53^2 - 4(4.9)(-4.21)}}{2(4.9)}[/tex]
[tex]t \approx 1.10 ~ s[/tex]
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Subject: Physics
Chapter: Kinematics
Keywords: Velocity , Driver , Car , Deceleration , Acceleration , Obstacle , Speed , Time , Rate
If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? express your answer in microseconds to two significant figures.
Answer:
Observed lifetime [tex]= 3.0\mu s[/tex]
Explanation:
The lifetime of muon in the muon’s reference frame.
[tex]t^{_{0}}=2.2\mu s[/tex]
The lifetime of muon in observer’s rest frame.
[tex]t=\gamma t_{0}[/tex]
Here the
[tex]\gamma =\dfrac{1}{\sqrt{1-\frac{V^2}{C^2}}}[/tex]
[tex]\gamma[/tex] is the relativistic factor.
V = Speed of muon
C = Speed of light
The muon’s speed of 70% of light speed.
Hence,
[tex]V=\dfrac{70}{100}C[/tex]
V = 0.7C
[tex]=\dfrac{1}{\sqrt{1-\frac{(0.7C)^2}{C^2}}}[/tex]
[tex]=\dfrac{1}{\sqrt{1-0.49}}[/tex]
[tex]=\dfrac{1}{\sqrt{0.51}}[/tex]
[tex]=\dfrac{1}{0.71}[/tex]
= 1.4
The lifetime of muon in observer’s rest frame.
[tex]t=\gamma t_{0}[/tex]
[tex]t=1.4\times 2.2\mu s[/tex]
[tex]t=3.0\mu s[/tex]
Further explanation:
The muon is a lepton which decays to form an electron or positron. The lifetime of the muon is 2.20 microseconds. The muon lifetime in the muon reference frame is .
But the observed lifetime [tex]= \gamma =\frac{1}{\sqrt{1-\frac{V^2}{C^2}}}[/tex]
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Keywords: Muon, Speed of light, life time.
you drop a glass on the floor and it shattters chemical or physical change ?
Find the kinetic energy of an electron whose de broglie wavelength is 34.0 nm.
Kinetic energy is a property of a moving item that is affected by both mass and velocity. The electron's kinetic energy with a de-Broglie wavelength of 34nm is 2.06 × [tex]10^-^2^2[/tex]J.
First, we have to convert de Broglie wavelength in m to satisfy the dimensions.
λ = 34.0nm =34×[tex]10^-^9[/tex].
To find kinetic energy we need to find velocity and for that, we need to find momentum by using the formulae:
P= h/λ = 6.6×[tex]10^-^3^4[/tex]/34×[tex]10^-^9[/tex] = 1.94×[tex]10^-^2^6[/tex] kgm/s.
After getting momentum we need to find the velocity
V=p/m = 1.94×[tex]10^-^2^6[/tex] / 9.1×[tex]10^-^3^1[/tex]= 2.13×[tex]10^4[/tex] m/s.
Now we have the value of velocity and by applying it [tex]k=1/2mv^2[/tex], we can find easily find the kinetic energy
[tex]k=1/2mv^2[/tex] = 1/2 (9.1×[tex]10^-^3^1[/tex] kg)×(2.13×[tex]10^4[/tex] m/s[tex])^2[/tex] = 2.06×[tex]10^-^2^2[/tex]J.
Therefore, the kinetic energy of the particle is 2.06×[tex]10^-^2^2[/tex]J.
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A crying baby emits sound with an intensity of 8.0 × 10-8 w/m2. calculate a reasonable estimate for the intensity level from a set of quintuplets (five babies), all crying simultaneously at the same place? the lowest detectable intensity is 1.0 × 10-12 w/m2.
The intensity level from a set of quintuplets (five babies) : 56 dB
Further explanationWave intensity is the power of a wave that is moved through a plane of one unit that is perpendicular to the direction of the wave
Can be formulated
[tex]\rm I=\dfrac{P}{A}[/tex]
I = intensity, W m⁻²
P = power, watt
A = area, m²
The farther the distance from the sound source, the smaller the intensity
[tex]\rm \dfrac{I_2}{I_1}=\dfrac{(r_1)^2}{(r_2)^2}[/tex]
So the intensity is inversely proportional to the square of the distance from the source
[tex]\rm I\approx \dfrac{1}{r^2}[/tex]
Intensity level (LI) can be formulated
[tex]\rm LI=10\:log\dfrac{I}{I_o}[/tex]
Io = 10⁻¹²
For the level of intensity of several sound sources as many as n pieces can be formulated:
LIn = LI1 + 10 log n
The intensity level of 1 baby is
[tex]\rm LI=10\:log\dfrac{8.10^{-8}}{10^{-12}}[/tex]
LI = 10 log 8.10⁴
LI = 49
The intensity level of 5 babies :
LI5 = LI + 10 log n
LI5 = 49 + 10 log 5
LI5 = 49 + 7
LI5 = 56
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Apply: what will be the total resistance and current in a parallel circuit with a 15-volt battery and three 10-ohm resistors? test your answers with the gizmo.
The total resistance in the parallel circuit with three 10-ohm resistors and a 15-volt battery is approximately 3.33 ohms. The total current through the circuit is approximately 4.50 amps.
To calculate the total resistance in a parallel circuit with three resistors of 10 ohms each, we use the formula for parallel resistance:
[tex]\frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}[/tex]
Substituting the values:
1/Rtotal = 1/10 + 1/10 + 1/10
1/Rtotal = 3/10
Therefore, Rtotal = 10/3 = 3.33 ohms
Next, we calculate the total current using Ohm's Law:
I = V/Rtotal
Given the battery voltage is 15 volts:
I = 15/3.33 ≈ 4.50 amps
The total resistance in the parallel circuit with three 10-ohm resistors and a 15-volt battery is approximately 3.33 ohms. The total current through the circuit is approximately 4.50 amps.
Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. mastering
What is the resistance of a 1500 w ( 120 v) hair dryer?
b. what is the current in the hair dryer when it is used?
Ohm's law claims that the voltage across a conductor is directly proportional to the current flowing through it.
(a) The resistance of the hairdryer will be 9.6 ohms.
(b)the current in the hairdryer will be 12.5 A.
When all physical parameters and temperature are constant,
Ohm's law claims that the voltage across a conductor is directly proportional to the current flowing through it.
This current-voltage connection may be expressed mathematically as,
The Equation of Ohm's Law
V=IR
(a)
The following data are given as
P = 1500 w
v = 120 v
The power generated in the hairdryer
[tex]\rm{P = vI}\\\\I=\frac{P}{v} \\\\I=\frac{1500}{120}\\\\I=12.5 A}[/tex]
To obtained the resistance
[tex]\rm R=\frac{v}{I} \\\\\rm R=\frac{120}{12.5} \\\\R= 9.6 ohm}[/tex]
Hence the resistance of the hairdryer will be 9.6 ohms.
(b)
The Equation of Ohm's Law
V=IR
[tex]\rm I =\frac{V}{R} \\\\\rm I =\frac{120}{9.6}\\\\\ I= 12.5 A[/tex]
Hence the current in the hairdryer will be 12.5 A.
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Calculate the weight ofa 58 kg astronaut on the moon where g=1.6 m/s2
Discuss five ways human activity has accelerated soil erosion
Answer:
road erosion, house construction, steep slope cultivation, tourism development, and animal trampling.
Explanation:
Two moles of an ideal gas are compressed in a cylinder at a constant temperature of 80.0 ∘c until the original pressure has tripled. calculate the amount of work done by gas.
The work done by two moles of an ideal gas compressed isothermally in a cylinder can be calculated using the formula W = nRT ln(V1/V2). The work is generally negative as the gas does work on its surroundings during the process.
Explanation:When an ideal gas is compressed in a cylinder, the work done by the gas can be calculated using the principles of thermodynamics. Specifically, if the gas is compressed isothermally (at a constant temperature), the work done by the gas during this process can be calculated using the formula W = nRT ln(V1/V2), where n represents the number of moles of gas, R is the universal gas constant, T is the temperature in Kelvin, and V1 and V2 are the initial and final volumes of the gas respectively.
In the scenario presented, we have 2 moles of gas, a temperature of 80.0°C, and the original pressure being tripled during the compression. This tripling of pressure corresponds to reduction in volume to one third. From these values, we can calculate the work done by the gas during compression. However, we do not have specific information about the volumes or pressures, so we cannot calculate a numerical value. In general, though, we can say the work done by the gas during an isothermal process is negative, as it is compressed and does work on its surroundings.
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The electric current running through the wire coil in an electric motor exerts force directly onto A) the battery. B) an aluminum axle. C) a powerful magnet. D) a rubber insulator.
Answer:
C) a powerful magnet
Explanation:
The electric current running through the wire coil in an electric motor exerts force directly onto A) the battery. B) an aluminum axle. C) a powerful magnet. D) a rubber insulator.
when current is pass to the coil, an electromagnetic force field is produced. The electromagnetic force field produced then have an impact on the magnet which drives the shaft to move
Jupiter‘s great red spot is believed to be a
Cyclonic storm -gradpoint
A camera with a 50.0-mm focal length lens is being used to photograph a person standing 3.00 m away. if the film is 36.0 mm high, what fraction of a 1.75-m-tall person will fit on it?
If a hydrogen atom in the ground state absorbs a photon of energy 12.09 ev, to which state will the electron make a transition?
Thermodynamics is the study of the relationship between thermal energy and mass. other forms of energy. types of engines. temperature.
Other forms of energy.
1) A substance has a half life of 20 years. what percentage would be left after 40 years?
2)After 4 half lifes of uranium, 10 grams of the uranium remains. how much uranium did you start with?
In a typical lightning strike, 2.9 c flows from cloud to ground in 0.18 ms. what is the current during the strike?
The absolute (or total) pressure at the bottom of a cylindrical container with a cross-sectional area of 47.0 cm2 and holding a fluid of density 560 kg/m3 is 115 kpa. (a) determine the depth of the fluid.
The fluid's depth in the cylinder can be determined using the equation for fluid pressure, h = P / (pg), and plugging in given values, resulting in an approximated depth of 20.9 meters.
Explanation:The total absolute pressure at a point in a fluid is the sum of the atmospheric pressure and the pressure due to the fluid above the point of reference. The latter is given by the equation P = pgh, where p is the density of the fluid, g is the acceleration due to gravity and h is the height (or depth) of the fluid column above the point of reference. In this scenario, we know P (absolute pressure, 115 kPa), p (density, 560 kg/m3), and g (standard gravity, roughly 9.81 m/s2), and we want to find h.
To find h, we can rearrange our equation: h = P / (pxg) . Plugging the given values we have h=115000Pa/(560kg/m3*9.8m/s2), which gives h = 20.9 m.
This means the depth of the fluid in the cylinder is approximately 20.9 meters.
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If a chromosome on unfolds itself how is transcription enhanced
Which forces tend to slow down an object
The measurement of an exoplanet's radius is measured in units compared to ________.
the Sun's radius
planet Earth's radius
planet Jupiter's radius
the moon's radius