Answer:
2.11 m
Explanation:
Given data
h=6.626×[tex]10^{-34\\}[/tex](plank constant)
L=45.7 pm
n=n2-n1
n=5-1
n=4
where,
n2=5
n1=1
To find:
E=?
λ=? (Wavelength)
solution
The energy stored in an electron at a specified level is given by;
E=[tex]h^{2}[/tex]×[tex]n^{2}[/tex]÷8m[tex]l^{2}[/tex]..........(1)
m=mass of electron(9.1×[tex]10^{-31}[/tex])
l=length of box
To find E
putting the value of given data in eq(1)
E=9.41×[tex]10^{-16}[/tex]
To find λ
λ=hc/E............................(2)
c=3×[tex]10^{8}[/tex](speed of light)
putting the value in eq 2 to find wavelength
λ=2.11 m
Note:
There is a chance in calculation error. but the method is correct to solve the problem.
Answer: wavelength λ = 2.9Å
Explanation:
Using the particle in a box model. The energy level level increases with n^2
En = (n^2h^2)/ 8mL^2 .....1
For the ground state, n = 1 to level n= 5, the energy level changes from E1 to E5
∆E = (5^2 - 1^2)h^2/8mL^2
but 5^2 - 1^2 = 24.
so,
∆E = 24h^2/8mL^2 .....2
And the wavelength of the radiation can be derived from the equation below:
E = hc/λ
λ = hc/E .......3
Substituting equation 2 to 3
λ = hc/[(24h^2)/ 8mL^2]
λ = 8mcL^2/(24h)
λ = 8mcL^2/24h .....4
Where,
n = energy state
h = Planck's constant = 6.626 × 10^-34 Js
m= mass of electron = 9.1 × 10^-31 kg
L = length = 45.7pm = 45.7×10^-12 m
E = energy
c= speed of light = 3.0 ×10^8 m/s
λ= wavelength
Substituting the values into equation 4 above
λ = [(8×9.1×3×45.7^2)/(24×6.626)] × 10^(-31+8-24+34)
λ = 2868.285390884 × 10^-13 m
λ = 2.9 × 10^-10 m
λ = 2.9Å
