Question

If a hydrogen atom is in the (n=4) state, how much energy is needed to ionize it?

a) (13.6 , {eV})
b) (2.55 , {eV})
c) (5.85 , {eV})
d) (8.32 , {eV})

Answer 1

The energy required to ionize a hydrogen atom from its nth energy level (n=4, in this case) can be calculated using the ionization energy formula
`\[ E_{\text{ionization}}` = -13.6 eV ×
`\left((1)/(n^2)\right)`. If a hydrogen atom is in the (n=4) state, the much energy is needed to ionize it is 0.85 eV. Therefore, none of the provided options match the correct value.

Step-by-step explanation:

The energy required to ionize a hydrogen atom from its nth energy level (n=4, in this case) can be calculated using the ionization energy formula:

`\[ E_{\text{ionization}}` = -13.6 eV ×
`\left((1)/(n^2)\right)`

Substitute n=4 into the formula:

`\[ E_{\text{ionization}}` = -13.6 eV ×
`\left((1)/(4^2)\right)`

`\[ E_{\text{ionization}}` = -13.6 eV ×
`\left((1)/(16)\right)`

`\[ E_{\text{ionization}}` = -13.6 eV × 0.0625

`\[ E_{\text{ionization}}` = -0.85 eV

Since ionization energy is a positive quantity, the absolute value is taken:

`\[ E_{\text{ionization}}` = 0.85 eV

If a hydrogen atom is in the (n=4) state, the much energy is needed to ionize it is 0.85 eV.

Therefore, none of the provided options match the correct value.