Question

A particle of mass 0.65 MeV/c 2 has kinetic energy 120 eV. Find its de-Broglie
wavelength, group velocity and phase velocity of the de-Broglie wave where c is
the velocity of light.

Answer 1

Explanation:

Because flashlights/torches operate on batteries which generally provide just a few volts (typically 1.5–6 VDC), and because of the limited capacity (in mAH) of those batteries, flashlight bulbs typically consume between fractions of a watt (W) to several watts of power at most, which in turn limits the light output/

Answer 2

Answer:

The de Broglie wavelength of the particle is 2.18 x $10^{-10$ m, the group velocity cannot be calculated without knowing the frequency, and the phase velocity depends on the frequency.

Explanation:

From the above question,

They have given :

A particle of mass 0.65 MeV/c 2 has kinetic energy 120 eV. Find its de-Broglie wavelength, group velocity and phase velocity of the de-Broglie wave where c is the velocity of light.

The de Broglie wavelength of a particle with mass m and kinetic energy E can be calculated using the equation:

λ = h / √(2mE)

where h is Planck's constant (h = 6.63 x $10^{-34$ Js).

The group velocity and phase velocity of a wave with wavelength λ and frequency f can be calculated using the equations:

v_group = dλ / dt = $c^{2$ / v_phase

v_phase = λf

To calculate the kinetic energy in joules, we can convert the energy from electron volts to joules:

            E = 120 eV * 1.6 x 10^-19 J/eV = 1.92 x $10^{-17$ J

To calculate the mass in kilograms, we can convert the mass from MeV/$c^{2$ to kg:

            m = 0.65 MeV/c^2 * 1.78 x $10^{-27$ kg/MeV

               = 1.15 x $10^{-27$ kg

Substituting these values into the equation for the de Broglie wavelength, we get:

            λ = h / √(2mE)

               = 6.63 x $10^{-34$ Js / √(2 * 1.15 x $10^{-27$ kg * 1.92 x $10^{-17$ J)

               = 2.18 x $10^{-10$ m

Substituting the wavelength into the equation for the group velocity,

we get:

             v.group = $c^{2}$ / v_phase = $c^{2}$ / (λf)

                           = (3 x 10^8 m/s)$.^{2}$ / (2.18 x   $10^{-10}$ m * f)

Substituting the wavelength into the equation for the phase velocity, we get:

            v.phase = λf = 2.18 x $10^{-10}$ m * f

So the de Broglie wavelength of the particle is 2.18 x $10^{-10$ m, the group velocity cannot be calculated without knowing the frequency, and the phase velocity depends on the frequency.

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