Chapter 41: Q. 42 (page 1208)

a few energy levels of the mercury atom.
a. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate the photon wavelength, in $n m$ .
b. What minimum speed must an electron have to excite the $492 n m$ wavelength blue emission line in the $H g$ spectrum?

Short Answer

Expert verified

$1.8 \times 10^{4} m$ is the final answer.

Step by step solution

Part (a) Step 1:

To find the allowed transitions, we need to use the selection rule $∆ l = \pm 1$

Using this rule we can have the following transitions:

$6 p \to 6 s, 7 s \to 6 p, 6 d \to 6 p, 7 p \to 7 s 8 s \to 6 p, 8 s \to 7 p, 8 p \to 6 s, 8 p \to 7 s 8 s \to 8 s$

Wavelength of photon:

Wavelength of the photon emitted in each transition

$λ = \frac{1240 e V n m}{∆ E e V}$

So we can have the following table:

Transition	$E_{2}$	$E_{1}$	$λ = \frac{1240 e V n m}{(E_{2} - E_{1}) e V}$
$6 p \to 6 s$	$6.7 e V$	$0 e V$	$185 n m$
$7 s \to 6 p$	$7.92 e V$	$6.7 e V$	$1015 n m$
$6 d \to 6 p$	$8.84 e V$	$6.7 e V$	$580 n m$
$7 p \to 6 s$	$8.84 e V$	localid="1648630398367" $0 e V$	$140 n m$
$7 p \to 7 s$	$8.84 e V$	$7.92 e V$	$1348 n m$
$8 s \to 6 p$	$9.22 e V$	$6.7 e V$	$492 n m$
$8 p \to 6 d$	$9.53 e V$	$8.84 e V$	$1797 n m$
$8 p \to 6 s$	$9.53 e V$	$0 e V$	$130 n m$
$8 p \to 7 s$	$9.53 e V$	$7.92 e V$	$770 n m$
$8 p \to 8 s$	$9.53 e V$	$9.22 e V$	$3999 n m$

Part (b) Step 2:

A photon of wavelength $492 n m$ is emitted when an electron in an $H g$ atom jumps from the $8 s$ state to the $6 p$ state.

The kinetic energy of the electron must be equal to the energy of the $8 s$ state

$\frac{1}{2} m v^{2} = 9.22 e V$

$m$ is the mass of an electron $= 9.1 \times 10^{31} k g$

Final equation step:

$v = \sqrt{\frac{(2) (9.22 e V) (1.6 \times 10^{- 19} j / e V)}{(9.1 \times 10^{- 31} k g)}} = 1.8 \times 10^{6} m / s$

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Short Answer

Step by step solution

Part (a) Step 1:

Wavelength of photon:

Part (b) Step 2:

Final equation step:

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a few energy levels of the mercury atom.a. Make a table showing all the allowed transitions in the emission spectrum. For each transition, indicate the photon wavelength, in nm.b. What minimum speed must an electron have to excite the 492nmwavelength blue emission line in the Hgspectrum?

Short Answer

Step by step solution

Part (a) Step 1:

Wavelength of photon:

Part (b) Step 2:

Final equation step:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Modern Physics

Dynamics

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Fundamentals of Physics

Nuclear Physics

Study anywhere. Anytime. Across all devices.