solution:
You need to find the frequency, and they have already given you the wavelength. And since you already know the speed of light, you can use formula (2) to answer this problem. Remember to convert the nano meters to meters because the speed of light is in meters.
Answer:change in energy of the electron=3.052x 10^-19J
which energy level does it move= level 2 , n=2
Explanation:
Using the formulae
1/λ = R (1/n1²- 1/n2²)
Where λ= 656.27 nm
1 nm = 1 x 10^-9 m
656.27 nm = 656.27 x 1 x 10^-9 =6.5726 x 10^-7
R =Rydberg constant = 1.0967 x 10^7m-1
1/λ = R (1/n1²- 1/n2²)
1/6.5726 x 10^-7=1.0967 x 10^7(1/n1²- 1/3²)
1/n1²=(1/6.5726 x 10^-7 x 1/1.0967 x 10^7) + 1/9
1/n1²=1,521,467.9 x 9.118x10^-8 + 0.1111
1/n1² =0.2498
n1²= 1/0.2498 =4
n1= = 2
it moves to energy level 2
b) Change in energy =ΔE = Rhc (1/n1²- 1/n2²)
Where R==Rydberg constant = 1.0967 x 10^7m-1
h = Planck constant = 6.626x 10^-34js
c = speed of light = 3.0 x 10^8 x m/s
ΔE = Rhc (1/n1²- 1/n2²)
=1.0967 x 10^7m-1 x6.626x 10^-34js X 3.0 x 10^8 x m/s (1/2² - 1/3²)
=2.18 x 10-18 x ( 1 /4 - 1/9)
=3.052x 10^-19J