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Chapter 39: Q37P (page 1216)

A neutron with a kinetic energy of 6.0 eV collides with a stationary hydrogen atom in its ground state. Explain why the collision must be elastic鈥攖hat is, why kinetic energy must be conserved. (Hint: Show that the hydrogen atom cannot be excited as a result of the collision.)

Short Answer

Expert verified

The neutron, with a kinetic energy of 6.0 eV does not have enough energy to excite the hydrogen atom.

Step by step solution

01

The energy of the photon emitted by a hydrogen atom:

The expression of the energy of the photon emitted for a hydrogen atom jumps from a state of to is given by,

E=13.6eV(1n12-1n12) 鈥�.. (1)

02

Explain the reason why the collision must be elastic and kinetic energy must be conserved

Substitute for and for in equation (1).

E=13.6eV1(1)2-1(2)2=13.6eV34=10.2eV

This is the minimum energy that the hydrogen atom can accept in order to jump to the first excited state. The neutron, with a kinetic energy of does not have enough energy to excite the hydrogen atom, therefore all the kinetic energy of the neutron will be transferred to the hydrogen atom as kinetic energy in form of an elastic collision.

Hence, the collision must be elastic and kinetic energy must be conserved.

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Most popular questions from this chapter

An electron is confined to a narrow-evacuated tube of length 3.0 m; the tube functions as a one-dimensional infinite potential well. (a) What is the energy difference between the electron鈥檚 ground state and its first excited state? (b) At what quantum number n would the energy difference between adjacent energy levels be 1.0 ev-which is measurable, unlike the result of (a)? At that quantum number, (c) What multiple of the electron鈥檚 rest energy would give the electron鈥檚 total energy and (d) would the electron be relativistic?

(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?

A hydrogen atom is excited from its ground state to the state with n=4. (a) How much energy must be absorbed by the atom? Consider the photon energies that can be emitted by the atom as it de-excites to the ground state in the several possible ways. (b) How many different energies are possible; What are the (c) highest, (d) second highest, (e) third highest, (f) lowest, (g) second lowest, and (h) third lowest energies.

The wave functions for the three states with the dot plots shown in Fig. 39-23, which have n = 2 , l = 1 , and 0, and ml=0,+1,-1, are

唯210(r,胃)=(1/42蟺)(a-3/2)(r/a)r-r/2acos胃唯21+1(r,胃)=(1/8蟺)(a-3/2)(r/a)r-r/2a(蝉颈苍胃)e+颈蠒唯21-1(r,胃)=(1/8蟺)(a-3/2)(r/a)r-r/2a(蝉颈苍胃)e-颈蠒

in which the subscripts on 唯(r,胃) give the values of the quantum numbers n , l , and ml the angles 胃and 蠒 are defined in Fig. 39-22. Note that the first wave function is real but the others, which involve the imaginary number i, are complex. Find the radial probability density P(r) for (a)唯210 and (b)唯21+1 (same as for 唯21-1 ). (c) Show that each P(r) is consistent with the corresponding dot plot in Fig. 39-23. (d) Add the radial probability densities for 唯210 , 唯21+1 , and唯21-1 and then show that the sum is spherically symmetric, depending only on r.

In the ground state of the hydrogen atom, the electron has a total energy of -13.06 eV. What are (a) its kinetic energy and (b) its potential energy if the electron is one Bohr radius from the central nucleus?
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