Question

kinetic energy of sub atomic particle is 5.85 ×10^-25J. calculate frequency of particle wave

Answer 1

In this Question,
3 Important formulas are to be used.

p=√2×K×m    ............where p is momentum, K is Kinetic Energy and m is mass.

λ=h/p  ..................  where h is Planck's constant with value h= 6.62607004 × 10-34 m2 kg / s

ν=c/λ ...................where c is 3 × 10⁸ m/s

Use First formula to calculate the the momentum(p) of the particle
then use second formula to calculate the De Brogile's Wavelengh (λ), then use the third formula to calculate Frequency(λ) of the Particle.

Answer 2

Hello Dear.

Here is your answer---

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.


Hope it helps.

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