Question

(0.5 point) Which possesses more energy a photon with a wavelength of 458 nm or a photon with a frequency of 3.84 x 1015 1/s?[6.17, 6.19, 6.21) (0.5 point) In which scenario will an atom absorb energy? a. when one of its electrons is moving closer to the nucleus b. when one of its electrons is moving further from the nucleus (1 point) When an electron in a hydrogen atom moves from the n= 7 to the n= 3 shell, a photon is released. What is the wavelength of the photon?[6.37,6.39, 6.45]

Answer 1

According to Planck's equation,

$E=h\nu =\frac{hc}{\lambda }$

where h is Planck's constant and is equal to $6.626\times 10^{-34} m^{2}kgs^{-1}$

$\small \nu$ is the frequency of a photon

c is the speed of light = $\small 3\times 10^{8} ms^{-2}$

and $\small \lambda$ is the wavelength of a photon

Case1: For $\lambda =458nm$ $\small \lambda =458nm=458\times 10^{-9}m$

$E=\frac{hc}{\lambda }=\frac{6.626\times 10^{-34}\times 3\times 10^{8}}{458\times 10^{-9}} J =4.34\times 10^{-15}J$

Case 2: For $\small \nu = 3.84\times 10^{15} s^{-1}$

$\small E=h\nu =6.626\times 10^{-34}\times 3.84\times 10^{15}=2.54\times 10^{-18}J$

Therefore, the photon with $\small \lambda =458nm$ have more energy