Question

Question 2.19 The electron energy in hydrogen atom is given by En = (–2.18 × 10–18)/n2 J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Class XI Structure of Atom Page 66

Answer 1

longest wavelength of light that can be used to cause this transition is 3.647×10^-5cm

Answer 2

concept : energy required to remove from nth orbit to infinity.
e.g., energy required to shift an electron from n = 2 to n = ∞.
$\triangle{E}=E_{ \infty }-E_2$
here A/C to question,
En = (-2.18 × 10^-18)/n² J
so,
∆E = (-2.18 × 10^-18 )/∞² - (-2.18 × 10^-18)/2²
= 2.18 × 10^-18/4 J
= 5.45 × 10^-19 J


now,
∆E = hc/λ
λ = hc/ ∆E
= 6.626 × 10^-34 Js × 3 × 10^8 m/s /5.45 × 10^-19 J
= 3.647 × 10^-7 m
= 364.7 × 10^-9 m
= 364.7 nm