Question

A hydrogen atom emits a photon corresponding to an electron transition from n=5 to n=1 the recoil speed of

Answer 1

the speed will be 4m/s......

Answer 2

The recoil speed is 4.36 m/s.

According to the Rydberg's equation,

1/λ = R(1/n₁² - 1/n₂²)

R is the Rydberg's constant = 1.097×10⁷ m⁻¹

λ is the wavelength and

n₁ = 1 and n₂ = 5.

Putting these values, we get:

1/λ = (1.097×10⁷)[1 - 1/25]

     = (1.097×10⁷)(24/25)

λ     = (1.097×10⁷)(24/25)⁻¹ = 9.5×10⁻⁸ m

Also, we know, momentum (p) = mv

where m is mass and v is velocity

and again p = h/λ

where h is Planck's constant = 6.626×10⁻³⁴ m² kg/s

So, h/λ = mv

⇒v = h/mλ

We have the value of h, and λ, and we know the mass of photon = 1.6×10⁻²⁷ kg.

Putting these values, we get:

v = (6.626×10⁻³⁴)/(1.6×10⁻²⁷ × 9.5×10⁻⁸) m/s

  = 4.36 m/s

Velocity = 4.36 m/s