Question

A hypothetical atom has three energy levels: the ground-state level and levels 1.50 eV and 5.00 eV above the ground state. What is the longest wavelength in the line spectrum for this atom? Let Planck's constant h = 4.136 x 10^-15 ev s, and the speed of light c = 3.00 x 10^8 m/s. (a)355 nm (b)780 nm (c)882 nm (d) 827 nm

Answer 1

option (d)

Step-by-step explanation:

E1 = 1.5 eV = 1.5 x 1.6 x 10^-19 J, E2 = 5 eV = 5 x 1.6 x 10^-19 J, c = 3 x 10^8 m/s, h = 6.62 x 10^-34 Js

Wavelength associated with 1.5 eV is λ1.

E1 = h c / λ1

λ1 = h c / E1

λ1 = (6.62 x 10^-34 x 3 x 10^8) / (1.5 x 1.6 x 10^-19)

λ1 = 8.275 x 10^-7 m = 827 nm

Wavelength associated with 5 eV is λ2.

E2 = h c / λ2

λ2 = h c / E2

λ2 = (6.62 x 10^-34 x 3 x 10^8) / (5 x 1.6 x 10^-19)

λ2 = 2.4825 x 10^-7 m = 248 nm

So, the longest wavelength is 827 nm