Question

Calculate the energy values of the electron in the second orbit of hydrogen
atom. What will be the radius of this orbit?

Answer 1

1. To find the energy of an electron with principal quantum number n we should use the formula:

E_n=-(Z²* k)/n²

Where Z –atomic number

k- Bohr constant, k= 2.179*10^-18 J

n- number of the energy level (principal quantum number)

For hydrogen atom Z=1, for an electron in the second orbit n=2

E₂= -((1)²*2.179*10^-18 J)/2² =-5.448*10^-19 J

2. Bohr radius for nth orbit is calculated according to the formula:

r_n = 0.529*n²/z

where n is a number of the orbit

z - atomic number

r₂ = 0.529*2² /1 = 0.529*4 = 2.116 Angstrom

Answer: 1. r₂ = 2.116 Angstrom, 2. E₂= -5.448*10^-19 J