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Chapter 41: Q. 22 (page 1207)

1.00脳106sodium atoms are excited to the 3pstate at t=0s. At what time have 8.0脳105photons been emitted ?

Short Answer

Expert verified

At 27ns,8.0脳105photons been emitted.

Step by step solution

01

Given Information

We have given that,

1.00脳106sodium atoms are excited to 3pstate at t=0s.

We have to find the time at which8.0脳105photons have emitted.

02

Simplification

From the table given below the sodium 3pstate has a lifetime of 蟿=17ns.

Some excited-state lifetimes

Atom State Lifetime(ns)
Hydrogen 2p 1.6
Sodium
 3p 17
Neon 3p 20
Potassium 4p 26

We know that, the number of excited atoms is given by

Nexc=N0e-t蟿(N0= No. of nuclei at t=0,蟿=time constant)

Every atom that transitions from the excited state to the ground state emits a photon, so the number Nof photons emitted is N=N0-Nexc=8.0脳105.. Therefore, the time at which Nphotons have been emitted is

N=N0-Nexc=N0(1-e-t/蟿)

t=蟿lnN0N0-N=(17ns)ln1.00脳1061.00脳106-0.8脳106=27ns

At localid="1650351508107" 27ns,8.0脳105been emitted.

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Most popular questions from this chapter

Find the distance, in terms of aB, between the two peaks in the radial probability density of the 2sstate of hydrogen.

Hint: This problem requires a numerical solution.

An atom in an excited state has a 1.0%% chance of emitting a photon in0.10ns . What is the lifetime of the excited state?

Two excited energy levels are separated by the very small energy difference 鈭�E. As atoms in these levels undergo quantum jumps to the ground state, the photons they emit have nearly identical wavelengths 位.

a. Show that the wavelengths differ by

鈭�位=位2hc鈭�E

b. In the Lyman series of hydrogen, what is the wavelength difference between photons emitted in the n=20to n=1transition and photons emitted in the n=21to n=1transition?

Prove that the normalization constant of the 1sradial wave function of the hydrogen atom is localid="1650358688008" 蟺aB3-1/2, as given in Equations 41.7.

A hydrogen atom is in the 2p state. How much time must elapse for there to be a 1.0% chance that this atom will undergo a quantum jump to the ground state?
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