Chapter 40: Q. 20 (page 1175)

An electron in a harmonic potential well absorbs a photon with a wavelength of $400 n m$ as it undergoes a $1 \to 2$ quantum jump. What wavelength is absorbed in a $1 \to 3$ quantum jump?

Short Answer

Expert verified

Wavelength absorbed in $1 \to 2$ quantum jump = $200 n m$

Wavelength absorbed in $1 \to 3$ quantum jump= $200 n m$

Step by step solution

Step 1. Given information

Energy level of harmonic quantum oscillator,

$E_{n} = (n - \frac{1}{2}) \frac{h ω}{2 π}$

Here,

n denotes the state,

$h =$ Planck's constant and

$ω =$ classical angular frequency.

Step 2. Quantum jump between 1→2

$E_{1} = (1 - \frac{1}{2}) \frac{h ω}{2 π}$

$= \frac{1}{2} (\frac{h ω}{2 π})$

$E_{2} = (2 - \frac{1}{2}) \frac{h ω}{2 π}$

$= \frac{3}{2} (\frac{h ω}{2 π})$

Now,

$λ_{photon, 1 \to 2} = \frac{h c}{\frac{3}{2} (\frac{h ω}{2 π}) - \frac{1}{2} (\frac{h ω}{2 π})}$

$= \frac{h c}{(\frac{h ω}{2 π})}$

$= \frac{2 π c}{ω}$

$\frac{2 π c}{ω} = 400 nm$

$\frac{π c}{ω} = 200 nm$

Step 3. Quantum jump between 1→3

$E_{1} = \frac{1}{2} (\frac{h ω}{2 π})$

$E_{3} = (3 - \frac{1}{2}) \frac{h ω}{2 π}$

$= \frac{5}{2} (\frac{h ω}{2 π})$

$λ_{photon, 1 \to 3} = \frac{h c}{\frac{5}{2} (\frac{h ω}{2 π}) - \frac{1}{2} (\frac{h ω}{2 π})}$

$= \frac{h c}{(\frac{4}{2}) (\frac{h ω}{2 π})}$

$= \frac{π c}{ω}$

As found earlier.

$\frac{π c}{ω} = 200 nm$

λ_{photon, 1 \to 3} = 200 nm

Thus, the wavelength absorbed in $1 \to 3$ quantum jump = $200 n m$

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An electron in a harmonic potential well absorbs a photon with a wavelength of $400 n m$ as it undergoes a $1 \to 2$ quantum jump. What wavelength is absorbed in a $1 \to 3$ quantum jump?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Quantum jump between 1→2

Step 3. Quantum jump between 1→3

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An electron in a harmonic potential well absorbs a photon with a wavelength of 400nmas it undergoes a 1→2 quantum jump. What wavelength is absorbed in a 1→3 quantum jump?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Quantum jump between 1→2

Step 3. Quantum jump between 1→3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Kinematics Physics

Fluids

Dynamics

Torque and Rotational Motion

Space Physics

Study anywhere. Anytime. Across all devices.

An electron in a harmonic potential well absorbs a photon with a wavelength of $400 n m$ as it undergoes a $1 \to 2$ quantum jump. What wavelength is absorbed in a $1 \to 3$ quantum jump?