Question

Calculate the minimum energy required to take an electron from the ground state to the first excited state in hydrogen atom
​

Answer 1

We have to find the minimum energy required to take an electron from the ground state to the first excited state in hydrogen atom.

According to Bohr's atomic theory,

energy required to remove an electron from nth orbit is given by,

$E_n=-13.6\times\frac{Z^2}{n^2} eV$

where Z is atomic number and n is orbit number.

for ground state, n = 1

for first excited state, n = 2

and atomic number for hydrogen atom, Z = 1

∴ minimum energy required to take an electron,

∆E = E₂ - E₁

= -13.6 × 1/2² - (-13.6 × 1/1²)

= -13.6/4 eV + 13.6 eV

= 13.6 eV - 3.4 eV

= 10.2 eV

Therefore the minimum energy required to take an electron from ground state to first excited state is 10.2 eV.