Question

In a muonic atom,a muon of mass of 200 times of that of an electron and same charge is bound to the proton. The wavelength of its Balmer series are in the range of:
(A)X rays
(B)INFRARED

$(c) \: \gamma \: rays$
(D) microwave​

Answer 1

Answer:

Correct answer is (B) INFRARED

Answer 2

Answer:

Explanation:

As we know that the, energy of an orbit is given by,

E=\frac{-me^{4}Z^{2}}{8\epsilon _{0}^{2}h^{2}n^{2}}E=  

8ϵ  

0

2

​  

h  

2

n  

2

 

−me  

4

Z  

2

 

​  

 

m = mass of electron

z = number protons/ Atomic no.

h = planks constant

n = no. of series / integer value

Since, Mass = 200 times of that of electron i.e. mμ = 200me

Energy directly proportional to mass

⇒ Energy increases by 200 times.

E=\frac{hc}{\lambda }\Rightarrow E\propto \frac{1}{\lambda }\Rightarrow \frac{E_{1}}{E_{2}}=\frac{\lambda _{2}}{\lambda _{1}}E=  

λ

hc

​  

⇒E∝  

λ

1

​  

⇒  

E  

2

​  

 

E  

1

​  

 

​  

=  

λ  

1

​  

 

λ  

2

​  

 

​  

 

Let E1 = E So, E2 = 200 E

\frac{E_{1}}{E_{2}}=\frac{\lambda_{2} }{\lambda _{1}}\Rightarrow \frac{\lambda_{2} }{\lambda _{1}}=\frac{E}{200E}  

E  

2

​  

 

E  

1

​  

 

​  

=  

λ  

1

​  

 

λ  

2

​  

 

​  

⇒  

λ  

1

​  

 

λ  

2

​  

 

​  

=  

200E

E

​  

 

\Rightarrow \lambda _{2}=\frac{1}{200}\lambda _{1}⇒λ  

2

​  

=  

200

1

​  

λ  

1

​  

 

Where λ2 = wavelength for corresponding Balmer series.

λ1 = wavelength for corresponding hydrogen atom.

⇒ Wavelength will decrease by 200 times.

So, the wavelength λ for correspondingBalmer series will be 1/200 times that of hydrogen atom, so it will be in range of X-rays.

Hence the correct option is (a).