Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Answers without the blur. Sign up and see all textbooks for free! → Illustration

Q16CQ

Expert-verified
Modern Physics
Found in: Page 279
Modern Physics

Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later
Illustration

Short Answer

Can the transition 2s→1s in the hydrogen atom occur by electric dipole radiation? The lifetime of the 2 s is known to be unusual. Is it unusually short or long?

Transition can’t occur by the electric dipole radiation. The electron will spend relatively long time in the 2 s before transitioning to the 1s. Thus, it is anticipated that the lifetime of the 2 s state be unusually long.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Significance of electric dipole radiation

The oscillating electric dipole is possibly the vital source for the electromagnetic radiations. The electric dipole is placed in a particular electric field and given with some disturbance to produce oscillations, that is responsible for producing the electromagnetic radiations.

Step 2: To determine transition of hydrogen atom from  occur by electric dipole radiation

From the selection rules of the electric dipole radiation, the change of / in the transition must be 1 or -1. Thus, the 2 s→1 s transition can't occur by the electric dipole radiation, since the change in / would be zero.

Since that the most efficient radiation is given by an oscillating electric dipole and it is known that the 2 s→1 s transition can't occur by electric dipole radiation. It is expected that the electron will spend relatively long time in the 2 s before transitioning to the 1s via other inefficient (unlike) types of radiation. Thus, it is anticipated that the lifetime of the 2s state be unusually long.

Therefore, transition can’t occur by the electric dipole radiation. The electron will spend relatively long time in the 2s before transitioning to the 1s. Thus, we anticipate that the lifetime of the 2s state be unusually long.

Most popular questions for Physics Textbooks

In general, we might say that the wavelengths allowed a bound particle are those of a typical standing wave,λ=2L/n , where is the length of its home. Given that λ=h/p, we would have p = nh/2L, and the kinetic energy, p2/2m , would thus be n2h2/8mL2. These are actually the correct infinite well energies, for the argumentis perfectly valid when the potential energy is 0 (inside the well) and is strictly constant. But it is a pretty good guide to how the energies should go in other cases. The length allowed the wave should be roughly the region classically allowed to the particle, which depends on the “height” of the total energy E relative to the potential energy (cf. Figure 4). The “wall” is the classical turning point, where there is nokinetic energy left: E = U. Treating it as essentially a one-dimensional (radial) problem, apply these arguments to the hydrogen atom potential energy (10). Find the location of the classical turning point in terms of E , use twice this distance for (the electron can be on both on sides of the origin), and from this obtain an expression for the expected average kinetic energies in terms of E . For the average potential, use its value at half the distance from the origin to the turning point, again in terms of . Then write out the expected average total energy and solve for E . What do you obtain

for the quantized energies?

At heart, momentum conservation is related to the universe being "translationally invariant," meaning that it is the same if you shift your coordinates to the right or left. Angular momentum relates to rotational invariance. Use these ideas to explain at least some of the differences between the physical properties quantized in the cubic three-dimensional box versus the hydrogen atom.

(a) What is the expectation value of the distance from the proton of an electron in a 3p state? (b) How does this compare with the expectation value in the 3 d state, calculated in Example 7.7? Discuss any differences.

In Appendix G. the operator for the square of the angular momentum is shown to be

L^2=-h2[cscθ∂∂θsinθ∂∂θ+csc2θ∂2∂ϕ2]

Use this to rewrite equation (7-19) as L^2⚇Φ=-Ch2⚇Φ

For states where l = n - t the radial probability assumes the general form given in Exercise 54. The proportionality constant that normalizes this radial probability is given in Exercise 64.

(a) Show that the expectation value of the hydrogen atom potential energy is exactly twice the total energy. (It turns out that this holds no matter what l may be)

(b) Argue that the expectation value of the kinetic energy must be the negative of the total energy.
Icon

Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Physics Textbooks

Work Energy and Power

Read explanation

Radiation

Read explanation

Astrophysics

Read explanation

Physics of Motion

Read explanation

Scientific Method Physics

Read explanation

Fluids

Read explanation

Torque and Rotational Motion

Read explanation

Nuclear Physics

Read explanation

Fields in Physics

Read explanation

Measurements

Read explanation

Space Physics

Read explanation

Electricity

Read explanation

Physical Quantities and Units

Read explanation

Medical Physics

Read explanation

Electrostatics

Read explanation

Further Mechanics and Thermal Physics

Read explanation

Mechanics and Materials

Read explanation

Engineering Physics

Read explanation

Energy Physics

Read explanation

Force

Read explanation

Particle Model of Matter

Read explanation

Waves Physics

Read explanation

Magnetism

Read explanation

Modern Physics

Read explanation

Atoms and Radioactivity

Read explanation

Dynamics

Read explanation

Electricity and Magnetism

Read explanation

Conservation of Energy and Momentum

Read explanation

Fundamentals of Physics

Read explanation

Kinematics Physics

Read explanation

Circular Motion and Gravitation

Read explanation

Linear Momentum

Read explanation

Rotational Dynamics

Read explanation

Oscillations

Read explanation

Translational Dynamics

Read explanation

Geometrical and Physical Optics

Read explanation

Thermodynamics

Read explanation

Magnetism and Electromagnetic Induction

Read explanation

Electromagnetism

Read explanation

Electric Charge Field and Potential

Read explanation

Turning Points in Physics

Read explanation

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.