Chapter 40: Q. 18 (page 1175)

Two adjacent energy levels of an electron in a harmonic potential well are known to be $2.0 e V$ and $2.8 e V$ . What is the spring constant of the potential well?

Short Answer

Expert verified

The spring constant for potential well= $1.4 N / m$

Step by step solution

Step 1. Given information

Energy level of quantum harmonic oscillator =

$E_{n} = (n - \frac{1}{2}) ℏ ω$

Here,

$n =$ denotes the state,

$ℏ$ = reduced Planck's constant and

$ω =$ classical angular frequency.

Adjacent energy level=

$E_{n + 1} = ((n + 1) - \frac{1}{2}) ℏ ω$

$= (n + \frac{1}{2}) ℏ ω$

Step 2. For the angular frequency

$= ℏ ω$

$ω = \frac{E_{n + 1} - E_{n}}{ℏ}$

$ω = \frac{2.8 eV - 2.0 eV}{1.05 \times 10^{- 34} J \cdot s}$

$= \frac{1.28 \times 10^{- 19}}{1.05 \times 10^{- 34} J \cdot s}$

width="126">=1.22×1015s-1

Step 3. For spring constant

$ω = \sqrt{\frac{k}{m}}$

Here,

$k =$ spring constant of the potential well

$m =$ electron mass.

$\frac{k}{m} = ω^{2}$

$k = m ω^{2}$

$k = (9.1 \times 10^{- 31} kg) {(1.22 \times 10^{15} s^{- 1})}^{2}$

$= 1.354 N / m \approx 1.4 N / m$

Thus, the spring constant for potential well = $1.4 N / m$

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Two adjacent energy levels of an electron in a harmonic potential well are known to be $2.0 e V$ and $2.8 e V$ . What is the spring constant of the potential well?

Short Answer

Step by step solution

Step 1. Given information

Step 2. For the angular frequency

Step 3. For spring constant

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Two adjacent energy levels of an electron in a harmonic potential well are known to be 2.0eV and 2.8eV. What is the spring constant of the potential well?

Short Answer

Step by step solution

Step 1. Given information

Step 2. For the angular frequency

Step 3. For spring constant

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Scientific Method Physics

Electricity and Magnetism

Rotational Dynamics

Conservation of Energy and Momentum

Quantum Physics

Study anywhere. Anytime. Across all devices.

Two adjacent energy levels of an electron in a harmonic potential well are known to be $2.0 e V$ and $2.8 e V$ . What is the spring constant of the potential well?