If 13.6ev energy is required to ionize the hydrogen atom,then the ener...
Calculation of the energy required to remove an electron from the first excited state of a hydrogen atom
To calculate the energy required to remove an electron from the first excited state of a hydrogen atom, we need to consider the energy levels of the hydrogen atom and the energy difference between these levels.
Here are the key points to consider:
1. Energy levels of the hydrogen atom:
- The ground state of a hydrogen atom is when the electron is in the lowest energy level, called the n=1 level.
- The first excited state is when the electron is in the n=2 level, which is a higher energy level than the ground state.
2. Energy difference between the levels:
- The energy difference between any two levels of a hydrogen atom can be calculated using the formula:
ΔE = 13.6/n^2 (in electron volts)
where ΔE is the energy difference and n is the principal quantum number of the higher energy level.
Now, let's calculate the energy required to remove an electron from the first excited state (n=2) of the hydrogen atom:
- Substitute n=2 into the formula:
ΔE = 13.6/2^2 = 13.6/4 = 3.4 eV
Therefore, the energy required to remove an electron from the first excited state of a hydrogen atom is 3.4 eV.
Answer
The correct option is C) 3.4 eV.