What are the energies in eV of quanta of wavelength? λ = 400, 500 and 700 nm? (Ans: 3.10 eV. 2.49 eV. 1.77 eV)



Data Given:

Let 

(1) λa = 400 nm = 400 ｘ 10⁻⁹ m 

(2) λb = 500 nm = 500 ｘ 10⁻⁹ m 

(3) λc = 700 nm = 700 ｘ 10⁻⁹ m 


∴ Plank's Constant = h =  6.62 ｘ 10⁻³⁴ m² kg s⁻¹

∴ Speed of light = 3 ｘ 10⁸ m s⁻¹


To Find:


(1) Ea =  ? (in eV)   

(2) Eb =  ? (in eV) 

(3) Ec =  ? (in eV) 


Solution:


The general formula for finding energy for a given wavelength λ is

E = hcλ 

where c is speed of light = 3 ｘ 10⁸ m s⁻¹


(1) Ea =  ? (in eV)  

Ea = hcλa

by putting values

Ea = 6.62ｘ10⁻³⁴m²kgs⁻¹ｘ3ｘ10⁸ms⁻¹c400ｘ10⁻⁹m 

Ea = 19.86ｘ10⁻²⁶m³kgs⁻²400ｘ10⁻⁹m

Ea = 0.04965ｘ 10⁻¹⁷ J

Ea = 4.965ｘ 10⁻¹⁹ J

Expressing in eV we have

Ea = 4.965ｘ10⁻¹⁹1.6ｘ10⁻¹⁹ eV

Ea = 3.103  eV --------------Ans.1




(2) Eb =  ? (in eV)  

Eb = hcλb 

by putting values

Eb = 6.62ｘ10⁻³⁴m²kgs⁻¹ｘ3ｘ10⁸ms⁻¹c500ｘ10⁻⁹m

Eb = 19.86ｘ10⁻²⁶m³kgs⁻²500ｘ10⁻⁹m

Eb = 0.03972ｘ 10⁻¹⁷ J

Eb = 3.972 10⁻¹⁹ J

Expressing in eV we have

Eb = 3.97210⁻¹⁹ｘ10⁻¹⁹1.6ｘ10⁻¹⁹ eV

Eb = 3.483  eV --------------Ans.2





(3) Ec =  ? (in eV)  

Ec = hcλb

by putting values

Ec = 6.62ｘ10⁻³⁴m²kgs⁻¹ｘ3ｘ10⁸ms⁻¹c500ｘ10⁻⁹m

Ec = 19.86ｘ10⁻²⁶m³kgs⁻²700ｘ10⁻⁹m

Ec = 0.02837ｘ 10⁻¹⁷ J

Ec = 2.837 ｘ 10⁻¹⁹ J

Expressing in eV we have

Ec = `\frac {2.837 ｘ 10⁻¹⁹ｘ 10⁻¹⁹ }{1.6 ｘ 10⁻¹⁹ }` eV

Ec = 1.773  eV --------------Ans.3

 


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