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olya-2409 [2.1K]
2 years ago
5

Calculate the wavelength of the electromagnetic radiation required to excite an electron from the ground state to the level with

n = 5 in a one-dimensional box 45.7 pm in length.
Physics
2 answers:
lana [24]2 years ago
8 0

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

anastassius [24]2 years ago
7 0

Answer:

2.11 m

Explanation:

<u>Given data</u>

h=6.626×10^{-34\\}(plank constant)

L=45.7 pm

n=n2-n1

n=5-1

n=4

<em>where,</em>

<em>n2=5</em>

<em>n1=1</em>

<u>To find:</u>

E=?

λ=? (Wavelength)

<u>solution</u>

The energy stored in an electron at a specified level is given by;

E=h^{2}×n^{2}÷8ml^{2}..........(1)

<em>m=mass of electron(9.1×</em>10^{-31})

<em>l=length of box</em>

<u>To find E</u>

putting the value of given data in eq(1)

E=9.41×10^{-16}

<u>To find λ</u>

λ=hc/E............................(2)

c=3×10^{8}(speed of light)

putting the value in eq 2 to find wavelength

λ=2.11 m

<u></u>

<u>Note:</u>

There is a chance in calculation error. but the method is correct to solve the problem.

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