What is the energy in Joules required to shift the electron of the hyd

1.	What is the energy in Joules required to shift the electron of the hydrogen atom from the Bohr orbit to the fourth Bohr orbit and what is the wavelength of light emitted, when electron returns to the ground state. The ground state electronic energy is −2.18 x 10-18J ?
Answer» \(\Delta\)E = 2.18 x 10^-18\(\Big[\frac{1}{n_1^2}-\frac{1}{n_2^2}\Big]\) Given n₁ = 1 and n₂ = 4 \(\Delta\)E = 2.18 x 10^-18\(\Big[\frac{1}{(1)^2}-\frac{1}{(4)^2}\Big]\) = 2.18 x 10^-18\(\Big[\frac{1}{1}-\frac{1}{16}\Big]\) = 2.18 x 10^-18\(\Big[\frac{16-1}{16}\Big]\) = 2.18 x 10^-18\(\big(\frac{15}{16}\big)\)J = 2.18 x 10^-18 J \(\therefore\) \(\Delta\)E = hv v = \(\frac{\Delta E}{h}\) = \(\frac{2.04\times10^{-18}}{6.626\times10^{-34}j\,sec}\) = 3.08 × 10¹⁵ Hz \(\lambda=\frac{c}{v}=\frac{3\times10^8ms^{-1}}{3.08\times10^{15}s^{-1}}\) = 9.7 × 10⁻⁸ m = 97 × 10⁻⁹ m = 97 nm

What is the energy in Joules required to shift the electron of the hydrogen atom from the Bohr orbit to the fourth Bohr orbit and what is the wavelength of light emitted, when electron returns to the ground state. The ground state electronic energy is −2.18 x 10-18J ?

Answer»

\(\Delta\)E = 2.18 x 10^-18\(\Big[\frac{1}{n_1^2}-\frac{1}{n_2^2}\Big]\)

Given n₁ = 1 and n₂ = 4

\(\Delta\)E = 2.18 x 10^-18\(\Big[\frac{1}{(1)^2}-\frac{1}{(4)^2}\Big]\)

= 2.18 x 10^-18\(\Big[\frac{1}{1}-\frac{1}{16}\Big]\)

= 2.18 x 10^-18\(\Big[\frac{16-1}{16}\Big]\)

= 2.18 x 10^-18\(\big(\frac{15}{16}\big)\)J

= 2.18 x 10^-18 J

\(\therefore\) \(\Delta\)E = hv

v = \(\frac{\Delta E}{h}\)

= \(\frac{2.04\times10^{-18}}{6.626\times10^{-34}j\,sec}\)

= 3.08 × 10¹⁵ Hz

\(\lambda=\frac{c}{v}=\frac{3\times10^8ms^{-1}}{3.08\times10^{15}s^{-1}}\)

= 9.7 × 10⁻⁸ m

= 97 × 10⁻⁹ m

= 97 nm