By de Broglie's wavelength ,lamda=h\mv orlamda = h\√2KEmwhere lamda is wavelengthh is Planck's constantm is mass of alpha particle (atomic mass of helium)KE is kinetic energy.

K. E=? Wavelength =12×10^-12m.We know that alpha particles are just helium ions He^2+.So mass of alpha particle = 4amu.Let us take the time taken by alpha particle to reach a particular distance be 'x'.c=distance /time =>3×10^8m/s=12×10^-12m / X sec.ON SOLVING WE WILL GETX=25×10^18 sec.So v=12×10^-12ms^-1/25×10^18=10^-28ms^-1/208.Now kinetic energy =1/2mv^2=4.622781e-61j.Hope it helped.From where did u find this question??

Kinetic Energy of an Alpha Particle with a Wavelength of 12 pm

To calculate the kinetic energy of an alpha particle with a wavelength of 12 pm, we can make use of the de Broglie wavelength equation and the relationship between kinetic energy and wavelength.

De Broglie Wavelength Equation:
The de Broglie wavelength equation relates the wavelength (λ) of a particle to its momentum (p) and mass (m):

λ = h / p

Where:
λ = wavelength
h = Planck's constant (6.626 x 10^-34 J·s)
p = momentum of the particle (kg·m/s)
m = mass of the particle (kg)

Relationship between Wavelength and Kinetic Energy:
The kinetic energy (KE) of a particle can be related to its wavelength through the following equation:

KE = (hc) / λ - Rest Energy

Where:
KE = kinetic energy
h = Planck's constant
c = speed of light
λ = wavelength
Rest Energy = rest energy of the particle

Calculating Momentum:
Since we are given the wavelength of the alpha particle (12 pm), we can use the de Broglie wavelength equation to calculate its momentum. The mass of an alpha particle is approximately 6.64 x 10^-27 kg.

λ = h / p
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 Kinetic Energy:
Now that we have the momentum, we can substitute it into the equation for kinetic energy in terms of wavelength.

KE = (hc) / λ - Rest Energy
KE = [(6.626 x 10^-34 J·s) * (3 x 10^8 m/s)] / (12 x 10^-12 m) - Rest Energy
KE = 1.6565 x 10^-15 J - Rest Energy

The rest energy of an alpha particle is approximately 3.73 x 10^-13 J.

KE = 1.6565 x 10^-15 J - 3.73 x 10^-13 J
KE ≈ -3.5545 x 10^-13 J

Conclusion:
The calculated kinetic energy of the alpha particle with a wavelength of 12 pm is approximately -3.5545 x 10^-13 J. It is important to note that the negative sign indicates that the alpha particle is in an energetically unfavorable state, suggesting that this value may not be physically meaningful.