Calculating Kinetic Energy of an Alpha Particle with a Wavelength of 12 Picometre

Understanding the Concept of Kinetic Energy and Wavelength

Kinetic energy is the energy an object possesses due to its motion. It can be calculated using the formula KE = 1/2mv², where m is the mass of the object and v is its velocity. Wavelength, on the other hand, is the distance between two consecutive peaks or troughs of a wave.

Using the De Broglie Equation

The De Broglie equation relates the wavelength of a particle to its momentum and mass. It is given by λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. Rearranging the equation, we get p = h/λ.

Calculating the Momentum of the Alpha Particle

We can use the De Broglie equation to find the momentum of the alpha particle. Given that its wavelength is 12 picometres, we have:

p = h/λ
p = 6.626 x 10^-34 J s / (12 x 10^-12 m)
p = 5.522 x 10^-22 kg m/s

Calculating the Kinetic Energy of the Alpha Particle

Now that we know the momentum of the alpha particle, we can use the formula for kinetic energy to calculate its value. The mass of an alpha particle is approximately 6.64 x 10^-27 kg.

KE = 1/2mv²
KE = 1/2 x 6.64 x 10^-27 kg x (5.522 x 10^-22 m/s)^2
KE = 9.11 x 10^-14 J

Therefore, the kinetic energy of the alpha particle with a wavelength of 12 picometres is 9.11 x 10^-14 J.

You know the formulae of kinetic energy = 1/2.mv^2 now here u have mass and lambda .
use this formulae lambda=velocity of light in vacuum/frequency
Here u get v(frequency) .And then put the values u get the answer.

lambda=c/v
12×10^-12=3×10^8/v
v=2.5×10^19
kinetic energy=1/2.mv^2
=1/2×6.64*10^-27*2.5×10^19
=8.3×10^-8 J