Question

The kinetic energy of a subatomic particle is 5.85*10^-25 J. Calculate the frequency of the particle wave.​

Answer 1

For Calculating Frequency of the Wave,

Using the Formula,

           ν = c/λ

Where, c = Speed of the Light.

           λ =  Wavelength.

           ν = Frequency.

For Calculating the Exact value, we need to calculate λ.

Given---

Kinetic energy(k) = 5.85 × 10^-25 J

Let the Mass of the Body be a kg.

Using the Formula,

Momentum(p) = √2 × k × a (mass of the sub-atomic particles)

                      = √2 × 5.85 × 10^-25 × a

                      = 8.27 × 10⁻²⁵ a

Also, λ =h/p

Where h = Plank Constant

              = 6.62 × 10⁻³⁴  m²kg/s

Now, λ = (6.62 × 10⁻³⁴)/(8.27 × 10⁻²⁵ × a)

           = (0.8009 × 10⁻⁹)/a

Now, using this,

              ν = c/λ

              ν = (3 × 10⁸)/{0.8009 × 10⁻⁹)/a}

              ν = (3.75 × 10¹⁷)/a Hz.

Thus, the Frequency of the Sub- Atomic Particles is (3.75 × 10¹⁷)/a Hz.

a is the mass of the sub-atomic particles. If the mass will be given, then the value can be accurately Calculated.

I Hope it will help you!!!

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