Question

Consider the following energy levels of a hypothetical atom:
E4____ -1.0 x 10^-19J
E3____ -5.0 x 10^-19J
E2____ -10 x 10^-19J
E1____ -15 x 10^-19J
(a) What is the wavelength of a photon needed to excite an electron from E1 to E4? (b) what is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? (c) When an electron drops E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.

Answer 1

a) ΔE = hc/λ
(-1 + 15) x 10⁻¹⁹ = 6.63 x 10⁻³⁴ x 3 x 10⁸ / λ
λ = 1.43 x 10⁻⁷ m

b) The energy is equivalent to difference in energy levels:
E3 - E2
= (-5 + 10) x 10⁻¹⁹ 
= 5 x 10⁻¹⁹ 

c) Change in energy = 10 x 10⁻¹⁹ J
10 x 10⁻¹⁹ = 6.63 x 10⁻³⁴ x 3 x 10⁸ / λ
λ = 1.99 x 10⁻⁷ m