1. Identify the state

The 5th excited state means: $n = 6$ because ground state is $n=1$, first excited is $n=2$, etc.

2. Use Bohr model energy relations for hydrogen atom

For an electron in a hydrogen atom:

• Total energy: $E = K + U$
• Potential energy: $U = -2K$
• Hence, $E = K + U = K - 2K = -K$

So the magnitude of potential energy is: $|U| = 2K$

Therefore, $\frac{K}{|U|} = \frac{K}{2K} = \frac{1}{2}$

3. Required ratio

The question asks for the ratio of the magnitude of kinetic energy to the potential energy. Interpreting this as: $\frac{\text{magnitude of kinetic energy}}{\text{magnitude of potential energy}} = \frac{K}{|U|} = \frac{1}{2}$

This ratio is independent of $n$, so even for the 5th excited state, it remains the same.

4. Check options

• A: $4$ ❌
• B: $1$ ❌
• C: $\frac{1}{2}$ ✅
• D: $\frac{1}{4}$ ❌

Therefore, the correct answer is: $\boxed{\frac{1}{2}}$