We wish to measure simultaneously the wavelength and position of a photon. Assume that the wavelength measurement gives 60.0 nm with an accuracy of 105 (i.e., Aλ/λ=106), what is the minimum uncertainty in the position of the photon?

We wish to measure simultaneously the wavelength and position of a photon. Assume that the wavelength measurement gives 60.0 nm with an accuracy of 105 (i.e., Aλ/λ=106), what is the minimum uncertainty in the position of the photon?

Modern Physics

3rd Edition

ISBN:9781111794378

Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer

Chapter5: Matter Waves

Section: Chapter Questions

Problem 20P

See similar textbooks

Related questions

Q: Suppose a laser pulse has an average duration of 5.00 femtoseconds and an average energy of 1.81 eV,…

A: Given : Average duration of the pulse, Δt = 5fs Average energy, E = 1.81 ev Uncertainty in energy,…

Q: Question 5 1) An electron is moving along x axis with the speed of 2x106 m/s (known with a precision…

A: Given data: The velocity of electron is v=2×106 m/s. The precision is x=0.5%. Mass of electron is…

Q: If an electron has an uncertainty in its velocity of 5.60 m/s, what is the uncertainty (in meters)…

Q: If an electron has an uncertainty in its position of 4.20 × 10-2 m, what is the uncertainty in its…

A: The objective of this question is to calculate the uncertainty in the velocity of an electron given…

Q: A measurement is made of a photon’s energy (from a laser) that results in an uncertainty in the…

Q: A sodium atom in one of the states labeled “Lowest excited levels” in Fig. remains in that state, on…

A: Given: The time taken by atom before transition ∆t = 1.6×10-8 s. The energy emitted by photon E =…

Q: An atom in an excited state of 4.7 eV emits a photon and ends up in the ground state. The lifetime…

A: Given Excited state Photon E= 4.7 eVExcited state life time =1.0×10-13 s.

Q: A 64.6 g ball moves at 38 m/s. If its speed is measured to an accuracy of 0.07%, what is the minimum…

Q: A spherical virus has a diameter of 50 nm. It is contained inside a long, narrow cell of length 1 x…

A: Given: The diameter of the spherical virus 50 nm. The length of the call is 1×10-4 m.

Q: The speed of an electron is measured to within an uncertainty of 2.0 × 104 m/s. What is the size of…

A: Operators in quantum mechanics are used to perform operations on the wave function. The momentum…

Q: A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the…

A: Given data: The energy is E=3.50 eV. The time is ∆t=2.0 ms. Part (a) The wavelength of the photon…

Q: A laser produces light of wavelength 625 nm in an ultrashort pulse. What is the minimum duration of…

A: Given: The wavelength of laser is λ=625 nm. The formula to calculate the energy of the photon is,…

Q: “Ultrafast” lasers produce bursts of light that last only on the order of 10 fs. Because of the…

A: Given data: The wavelength is λ=532 nm. The time interval is ∆t=10 fs. Part (a) According to the…

Q: The speed of an electron is measured to be 5.00 × 103 m/s to an accuracy of 0.003 00%. Find the…

A: It is given that,

Q: 2. If the speed of an electron is measured to within an uncertainty of 2.0×10ª m/s, what woul be the…

A: Given Data The speed of an electron is:∆V=2×104 m/s The mass of an electron is:me=9.11×10-31 kg…

Q: An electron is located on a pinpoint having a diameter of 6.11 µm. What is the minimum uncertainty…

Q: A beam of electrons travels at approximately 1.282x10° m/s and there is a 5.00% uncertainty in the…

A: Given data v=1.282×106 m/s Here, v is the velocity of the beam of the electrons. We have to apply…

Q: An electron is located on a pinpoint having a diameter of 2.5 µm. What is the minimum uncertainty in…

Q: Suppose the position of a chlorine ion in a membrane is measured to an accuracy of 0.75 μm. a) What…

Q: If the speed of an electron is measured to within an uncertainty of 2.0×10 4 m/s, what would be the…

Q: A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the…

A: (a) The energy and wavelength of the photon, The energy of the photon is 3.5 eV, The wavelength is…

Q: proton is accelerated to a speed of 2.10*10^5 m/s. If the uncertainty in the measured speed is 5%…

Q: A certain atom has an energy level 3.60 eV above the ground state. When excited to this state, atom…

A: Using Heisenberg's uncertainty relation, ∆E∆t≥ℏ

Q: What is the minimum uncertainty in position, in nm, of an electron whose velocity is known to be…

A: Given ∆ v =( 3.08-2.96) ×105 ∆ v = 0.12 ×105m/s

Q: What is the minimum uncertainty in position, in nm, of an electron whose velocity is known to be…

A: Given, V1 = 2.96 x 105 m/s V2 = 3.08 x 105 m/s (i) Uncertainty in velocity (ΔV) = (3.08 -2.96)x 105…

Q: assume that an electron is moving along the x-axis and that you measure its speed to be…

A: According to the Heisenberg Uncertainity principle, ∆x×∆v=h2πm .... (1) Where, h is the…

Concept explainers

Blackbody

Q.5 A blackbody radiates how much energy when the temperature of the body is elevated?

Question

We wish to measure simultaneously the wavelength and position of a photon. Assume that
the wavelength measurement gives 60.0 nm with an accuracy of 105 (i.e., Aλ/λ=106), what
is the minimum uncertainty in the position of the photon?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Introduce the formula of Heisenberg principle

VIEW

Step 2: Determine the given variables

VIEW

Step 3: Calculate the uncertainty of position

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A quantum mechanical oscillator vibrates at a frequency of 250.0 THz. What is the minimum energy of radiation it can emit?
What is the wavelength of (a) a 12-keV X-ray photon; (b) a 2.O-MeV y -ray photon?
At what velocity will an electron have a wavelength of 1.00 m?
What is the momentum of a 589-nm yellow photon?
Check Your Understanding A sodium atom nukes a transition from the first excited state the wound state, emitting a 589.0-nm photon with energy 2.105 eV. If the lifetime of this excited state is 16108s, what is the uncertainty in energy of this state? What is width of the corresponding line?
Suppose the position of a chlorine ion in a membrane is measured to an accuracy of 0.75 μm. a) What is its minimum uncertainty in velocity in meters per second, given its mass is 5.86 × 10-26 kg? b) If the ion is measured to have a velocity of 8.9 × 103 m/s, what is the uncertainty in its kinetic energy in electron volts?
A 64.6 g ball moves at 38 m/s. If its speed is measured to an accuracy of 0.07%, what is the minimum uncertainty in its position? Answer in units of m. S.
In designing an experiment, you want a beam of photons and a beam of electrons with thesame wavelength of 0.281 nm, equal to the separation of the Na and Cl ions in a crystal ofNaCl. Find the energy of the photons and the kinetic energy of the electrons in electrovolts(eV).
A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the atom remains for 2.0 ms, on aver- age, before it emits a photon and returns to the ground state. (a) What are the energy and wavelength of the photon? (b) What is the smallest possible uncertainty in energy of the photon?
Suppose a laser pulse has an average duration of 5.00 femtoseconds and an average energy of 1.81 eV, and it has an uncertainty of 13.8%. What is the highest energy you can observe for a photon in the pulse? (in eV)
If a proton has an uncertainty in its velocity of 5.90 × 10⁻⁴ m/s, what is the uncertainty (in meters) in its position?
If an electron has an uncertainty in its velocity of 5.60 m/s, what is the uncertainty (in meters) in its position?