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A proton accelerated from rest through a potential difference of 'V' volts has a wavelength λ associated with it. An alpha particle in order to have the same wavelength must be accelerated from rest through a potential difference of
- a)V volt
- b)4V volt
- c)2V volt
- d)V/8 volt
Correct answer is option 'D'. Can you explain this answer?
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A proton accelerated from rest through a potential difference of '...
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A proton accelerated from rest through a potential difference of '...
Of λ meters given by:
λ = h / √(2mE)
where h is the Planck constant, m is the mass of the proton, and E is the kinetic energy of the proton.
Since the proton is accelerated from rest, its initial kinetic energy is zero, so E = qV, where q is the charge of the proton. Substituting this into the equation above, we get:
λ = h / √(2mqV)
Since q and m are constants, we can simplify this expression as:
λ = h / √(2m) * 1/√V
Therefore, the wavelength of the proton is inversely proportional to the square root of the potential difference. As the potential difference increases, the wavelength decreases, and vice versa.
λ = h / √(2mE)
where h is the Planck constant, m is the mass of the proton, and E is the kinetic energy of the proton.
Since the proton is accelerated from rest, its initial kinetic energy is zero, so E = qV, where q is the charge of the proton. Substituting this into the equation above, we get:
λ = h / √(2mqV)
Since q and m are constants, we can simplify this expression as:
λ = h / √(2m) * 1/√V
Therefore, the wavelength of the proton is inversely proportional to the square root of the potential difference. As the potential difference increases, the wavelength decreases, and vice versa.
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A proton accelerated from rest through a potential difference of 'V' volts has a wavelength λassociated with it. An alpha particle in order to have the same wavelength must be accelerated from rest through a potential difference ofa)V voltb)4V voltc)2V voltd)V/8 voltCorrect answer is option 'D'. Can you explain this answer?
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