The angular momentum of an electron in hydrogen atom is `4 h// 2 pi`. Kinetic energy this electron is

Options

A. `4.35 eV`
B. `1.51 eV`
C. `0.85 eV`
D. `13.6 eV`

Explanation

To find the kinetic energy of the electron in a hydrogen atom given its angular momentum, we can follow these steps:

### Step 1: Understand the relationship between angular momentum and quantum number
The angular momentum \( L \) of an electron in a hydrogen atom can be expressed using Bohr's postulate as:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

### Step 2: Compare the given angular momentum with the formula
We are given that:
\[ L = 4 \frac{h}{2\pi} \]
By comparing this with the formula for angular momentum, we can equate:
\[ n \frac{h}{2\pi} = 4 \frac{h}{2\pi} \]
From this, we can deduce that:
\[ n = 4 \]

### Step 3: Calculate the total energy of the electron
The total energy \( E \) of an electron in the nth orbit of a hydrogen atom is given by:
\[ E = -\frac{13.6 \text{ eV}}{n^2} \]
Substituting \( n = 4 \):
\[ E = -\frac{13.6 \text{ eV}}{4^2} = -\frac{13.6 \text{ eV}}{16} = -0.85 \text{ eV} \]

### Step 4: Relate total energy to kinetic energy
In a hydrogen atom, the total energy \( E \) is related to kinetic energy \( KE \) by the equation:
\[ E = -KE \]
Thus, the kinetic energy can be expressed as:
\[ KE = -E \]
Substituting the value of \( E \):
\[ KE = 0.85 \text{ eV} \]

### Final Answer
The kinetic energy of the electron is \( 0.85 \text{ eV} \).

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