Which is the correct relation between energies of one electron species?
`E_1` =Energy of electron in the first Bohr orbit,
`E_2` =Energy of electron in the second Bohr orbit,
`E_3` =Energy of electron in the third Bohr orbit,
`E_4` =Energy of electron in the fourth Bohr orbit.

Options

A. `E_1 " of " H = 1//2E_2 of He^(+) = 1//3E_3 " of " Li^(2+) = 1//4E_4 " of " Be^(3+)`
B. `E_1 (H) = E_2 (He^(+)) = E_3 (Li^(2+)) = E_4 (Be^(3+))`
C. `E_1 (H) = 2E_2 (He^(+)) = 3E_3 (Li^(2+)) = 4E_4 (Be^(3+))`
D. None of the above relations are correct

Answer

B

Explanation

The energy of the nth Bohr orbit is given as follows:
`E_n = -13.6 xx(Z/n)^2 eV`
Where Z is the atomic number and n is the orbit number. From the formula, it is clear that the orbits having equal energy will have the same value of `Z/n` will have the same energy.
Calculating `Z/n` for
1) `E_1 (H) = 1/1 =1`
2) `E_2(He^(+)) =2/2 = 1`
3) `E_3 (Li^(2-)) =3/3 = 1`
4) `E_4 (Be^(+)) = 4/4 = 1`
Thus, all these orbits will have equal energies.