Question

1. The energy of the electron in the lowest level of the hydrogen atom (n=1) is -2.179×10-18 J. What is the energy of the electron in level n=5? -8.716×10-20 J 2.The electron in a hydrogen atom moves from level n=6 to level n=4.

a) Is a photon emitted or absorbed?

b) What is the wavelength of the photon?

Answer 1

Energy of an electron in n^th orbital is given by,

E= -(2.179x10^-18)/n² Joules

, therefore, we can write as,

=

therefore,

E₅ = (-2.179x10^-18)(1²/5²)

E₅ = -8.176x10^-20

a) as the electron energy is directly proportional to the square of the orbit number,

when the electron moves from n=6 to n=4,

its energy decreases, so it must have emitted a photon so that the energy will decrease.

b) E₆-E₄ = (E₁/n₆²) - (E₁/n₄²) (From above equations)

hence,

E₆-E₄ = 7.5659 x 10^-20 Joules

now this energy difference will be equal to (hc/)

where h = Planck's constant

c = velocity of light

= wavelength of photon

= hc / change in energy

=((6.634x10^-34)x(3x10⁸))/7.5659 x 10^-20

=2.63x10^-6 m