Chapter 41: Q. 3 (page 1206)

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

Short Answer

Expert verified

The maximum possible angular momentum $L$ is $\sqrt{20 h}$ .

Step by step solution

Given Information

We need to find the maximum possible angular momentum $L$ .

Simplify

Finding the maximum angular momentum $L$ of a hydrogen atom.

Consider:

$E = - 0.544 e V$

know that the hydrogen atom's energy is given as:

$E_{n} = - \frac{13.6 e V}{n^{2}}$

Using formula, find the value of $n$ :

$E_{n} = - \frac{13.6 e V}{n^{2}} - 0.544 e V = - \frac{13.6 e V}{n^{2}} (- 0.544 e V) \times n^{2} = - 13.6 e V n^{2} = \frac{- 13.6 e V}{- 0.544 e V} n^{2} = 25 n = \sqrt{25} n = 5$

Now, finding the maximum angular momentum $L$ .

Angular momentum $L$ is given as:

$L = \sqrt{l (l + 1) h}$

Then,

$L = \sqrt{l (l + 1) h} L = \sqrt{4 (4 + 1) h} L = \sqrt{4 (5) h} L = \sqrt{20 h}$

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

Short Answer

Step by step solution

Given Information

Simplify

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What is the maximum possible angular momentumL(as a multiple of h) of a hydrogen atom with energy-0.544eV?

Short Answer

Step by step solution

Given Information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Oscillations

Measurements

Further Mechanics and Thermal Physics

Nuclear Physics

Mechanics and Materials

Study anywhere. Anytime. Across all devices.

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