The ratio of the velocity of electron in 3rd and 5th orbit of hydrogen atom is

Options

A. `5:3`
B. `1:3`
C. `5:1`
D. `1:1`

Answer

To find the ratio of the velocity of an electron in the 3rd and 5th orbit of a hydrogen atom, we can use the formula for the velocity of an electron in a given orbit. The velocity \( V \) of an electron in the nth orbit of a hydrogen atom is given by:

\[ V = \frac{2.18 \times 10^6 \, Z}{n} \]

where:
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( n \) is the principal quantum number (the orbit number).

### Step 1: Calculate the velocity in the 3rd orbit
For the 3rd orbit, \( n_1 = 3 \):

\[ V_1 = \frac{2.18 \times 10^6 \, \times 1}{3} = \frac{2.18 \times 10^6}{3} \]

### Step 2: Calculate the velocity in the 5th orbit
For the 5th orbit, \( n_2 = 5 \):

\[ V_2 = \frac{2.18 \times 10^6 \, \times 1}{5} = \frac{2.18 \times 10^6}{5} \]

### Step 3: Find the ratio of velocities
Now we can find the ratio of the velocities \( \frac{V_1}{V_2} \):

\[ \frac{V_1}{V_2} = \frac{\frac{2.18 \times 10^6}{3}}{\frac{2.18 \times 10^6}{5}} = \frac{5}{3} \]

### Conclusion
Thus, the ratio of the velocity of the electron in the 3rd and 5th orbits of the hydrogen atom is:

\[ \frac{V_1}{V_2} = \frac{5}{3} \]

### Final Answer
The ratio of the velocity of the electron in the 3rd and 5th orbit of hydrogen atom is \( \frac{5}{3} \).

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