Question

In an atom X, electrons absorb the energy from an external source. This energy “excites” the electrons from a lower-energy level to a higher-energy level around the nucleus of the atom. When electrons return to the ground state, they emit photons.

Figure below is the energy level diagram of atom X with three energy levels, E₁ = 0.00 eV, E₂ = 1.78 eV and E₃ = 2.95 eV. The ground state is considered 0 eV for reference.

What wavelength of radiation is needed to excite the atom to energy level E₂ from E₁?

Answer 1

Given, E₁ ​= 0 eV, E₂ ​= 1.78 eV

h = 6.6 × 10⁻³⁴ J s, c = 3 × 10⁸ m s⁻¹

1 eV = 1.6 × 10⁻¹⁹ J

ΔE = E₂ − E₁

= 1.78 − 0

= 1.78 eV

Using, E = `(hc)/lambda`

`lambda = (hc)/(\DeltaE)`

= `(6.6 xx 10^-34 xx 3 xx 10^8)/(1.78 xx 1.6 xx 10^-19)`

= 6.95 × 10⁻⁷ m