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Chapter 41: Q. 7 (page 1207)

What are $E$ and $L$ (as a multiple of $h$ ) of a hydrogen atom in the $6 f$ state?

Short Answer

Expert verified

The hydrogen atom in the $6 f$ state is $E_{n} = - 0.3777 eV$ and $L = \sqrt{12} ħ$ .

Step by step solution

01

Given Information

We need to find are $E$ and $L$ (as a multiple of $h$ ) of a hydrogen atom in the $6 f$ state.

02

Simplify

Finding value for $E$ and $L$ of a hydrogen atom in the $6 f$ state.

know that the hydrogen atom in the $6 f$ state is described by $n = 6$ an $l = 3$ .

Then,

$E_{n} = \frac{- 13.6 eV}{n^{2}} E_{n} = \frac{- 13.6 eV}{6^{2}} E_{n} = \frac{- 13.6 eV}{36} E_{n} = - 0.3777 eV$

Now, finding the value for angular momentum $L$ :

$L = \sqrt{l (l + 1)} ħ L = \sqrt{3 (3 + 1)} ħ L = \sqrt{3 (4)} ħ L = \sqrt{12} ħ$

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Most popular questions from this chapter

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

a. Show that the wavelengths differ by

$∆ λ = \frac{λ^{2}}{h c} ∆ E$

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

In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short pulses of light, each containing $1.0 m J$ of energy.

a. There are $9.7 \times 10^{14}$ photons in each pulse. What is the wavelength of the laser?

b. Each pulse lasts a mere $20 n s$ . What is the average power delivered to the cornea during a pulse?

A laser emits $1.0 \times 10^{19}$ photons per second from an excited state with energy $E_{2} = 1.17 e V$ . The lower energy level is $E_{1} = 0 e V$ .

a. What is the wavelength of this laser?

b. What is the power output of this laser?

What is the maximum possible angular momentum $L$ (as a multiple of h) of a hydrogen atom with energy $- 0.544 e V$ ?

What is the angular momentum of a hydrogen atom in

(a) a $6 s$ state and

(b) a $4 f$ state? Give your answers as a multiple of U.

See all solutions

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