Question

the zeeman component of a 500nm spectral lines are 0.0116nm apart.when the magnetic fields is 1.00tesla.find the ratio of e/m for the electron from these data​

Answer 1

Given info : the zeeman component of a 500nm spectral lines are 0.0116nm apart. when the magnetic fields is 1.00 Tesla.

To find : The ratio of e/m for the electron from above data.

solution : The wavelength seperation is given by,

∆λ = eBλ²/4πmc

where ∆λ = 0.0116 nm = 1.16 × 10¯¹¹ m

λ = 500 × 10^-9 m = 5 × 10^-7 m

B = 1 Tesla

c = 3 × 10^8 m/s

so, 1.16 × 10¯¹¹ = e × 1 × (5 × 10^-7)²/(4 × 3.14 × m × 3 × 10^8)

⇒e/m = (1.16 × 10¯¹¹ × 4 × 3.14 × 3 × 10^8)/(25 × 10¯¹⁴)

= 1.748 × 10¹¹ C/kg

Therefore the ratio of e/m is 1.748 × 10¹¹ C/kg

Answer 2

Given info :

the zeeman component of a 500nm spectral lines are 0.0116nm apart. when the magnetic fields is 1.00 Tesla.

To find :

The ratio of e/m for the electron from above data.

solution :

The wavelength seperation is given by,

∆λ = eBλ²/4πmc

where ∆λ = 0.0116 nm = 1.16 × 10¯¹¹ m

λ = 500 × 10^-9 m = 5 × 10^-7 m

B = 1 Tesla

c = 3 × 10^8 m/s

so, 1.16 × 10¯¹¹ = e × 1 × (5 × 10^-7)²/(4 × 3.14 × m × 3 × 10^8)

⇒e/m = (1.16 × 10¯¹¹ × 4 × 3.14 × 3 × 10^8)/(25 × 10¯¹⁴)

= 1.748 × 10¹¹ C/kg

Therefore the ratio of e/m is 1.748 × 10¹¹ C/kg