The velocity of an electron in the nth orbit of hydrogen atom bears the ratio 1:411 to the velocity of light. The number of coloured lines formed when electron jumps from (n+3) state is:

A. 4

B. 3

C. 5

D. 6

To determine the number of colored lines formed when an electron jumps from the (n+3) state in a hydrogen atom, we need to understand how electron transitions between energy levels produce spectral lines. Each transition corresponds to a specific wavelength of light, which we perceive as color. Let's break this down step by step.

Understanding Electron Transitions

In a hydrogen atom, electrons occupy discrete energy levels, often referred to as orbits or shells. When an electron transitions from a higher energy level to a lower one, it emits energy in the form of light. The energy difference between these levels determines the wavelength (and thus color) of the emitted light.

Energy Levels in Hydrogen

The energy levels of a hydrogen atom can be described using the formula:

E_n = -13.6 eV/n²

where E_n is the energy of the nth level and n is the principal quantum number (1, 2, 3, ...). The electron can jump from a higher level (n+3) to any lower level (n, n-1, n-2, etc.).

Calculating Possible Transitions

When the electron is in the (n+3) state, it can transition to the following lower energy levels:

• n+2
• n+1
• n

From each of these levels, the electron can make further transitions down to lower levels. Let's analyze each transition:

1. Transition from (n+3) to (n+2)

This transition produces one spectral line.

2. Transition from (n+3) to (n+1)

This transition also produces one spectral line.

3. Transition from (n+3) to n

This transition produces another spectral line.

4. Additional Transitions from (n+2) and (n+1)

Now, we also need to consider transitions from the (n+2) and (n+1) states:

• From (n+2) to n (1 line)
• From (n+1) to n (1 line)

Summarizing the Lines

Now, let's tally up the total number of unique transitions:

• (n+3) to (n+2) - 1 line
• (n+3) to (n+1) - 1 line
• (n+3) to n - 1 line
• (n+2) to n - 1 line
• (n+1) to n - 1 line

This gives us a total of 5 unique transitions, which correspond to 5 colored lines.

Final Answer

Therefore, the number of colored lines formed when the electron jumps from the (n+3) state is 5. The correct option is C. 5.