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The wavelength of electrons accelerated from rest through a potential difference of 40 kV is X × 10-12 m. The value of X is _________. (Nearest integer)
Given: Mass of electrons = 9.1 × 10-31 kg
Charge on an electron = 1.6 × 10-19 C
Planck's constant = 6.63 × 10-34 Js
Given: Mass of electrons = 9.1 × 10-31 kg
Charge on an electron = 1.6 × 10-19 C
Planck's constant = 6.63 × 10-34 Js
Correct answer is '6'. Can you explain this answer?
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The wavelength of electrons accelerated from rest through a potential ...
Wavelength of electron is given by
Here q = charge on electron, v = potential difference
Here q = charge on electron, v = potential difference
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The wavelength of electrons accelerated from rest through a potential ...
To find the wavelength of electrons accelerated through a potential difference, we can use the de Broglie wavelength equation:
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the electrons.
The momentum of an electron can be calculated using the equation:
p = √(2mE)
where m is the mass of an electron (9.10938356 × 10^-31 kg) and E is the energy gained by the electrons due to the potential difference.
The energy gained by the electrons can be calculated using the equation:
E = qV
where q is the charge of an electron (1.602176634 × 10^-19 C) and V is the potential difference (40 kV = 40,000 V).
Substituting the values into the equations:
E = (1.602176634 × 10^-19 C)(40,000 V) = 6.408706536 × 10^-15 J
p = √(2(9.10938356 × 10^-31 kg)(6.408706536 × 10^-15 J)) = 5.047 x 10^-24 kg·m/s
Finally, substituting the value of p into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J·s) / (5.047 x 10^-24 kg·m/s) ≈ 1.31 x 10^-10 m
Therefore, the wavelength of electrons accelerated through a potential difference of 40 kV is approximately 1.31 x 10^-10 meters.
λ = h / p
where λ is the wavelength, h is the Planck's constant (6.626 x 10^-34 J·s), and p is the momentum of the electrons.
The momentum of an electron can be calculated using the equation:
p = √(2mE)
where m is the mass of an electron (9.10938356 × 10^-31 kg) and E is the energy gained by the electrons due to the potential difference.
The energy gained by the electrons can be calculated using the equation:
E = qV
where q is the charge of an electron (1.602176634 × 10^-19 C) and V is the potential difference (40 kV = 40,000 V).
Substituting the values into the equations:
E = (1.602176634 × 10^-19 C)(40,000 V) = 6.408706536 × 10^-15 J
p = √(2(9.10938356 × 10^-31 kg)(6.408706536 × 10^-15 J)) = 5.047 x 10^-24 kg·m/s
Finally, substituting the value of p into the de Broglie wavelength equation:
λ = (6.626 x 10^-34 J·s) / (5.047 x 10^-24 kg·m/s) ≈ 1.31 x 10^-10 m
Therefore, the wavelength of electrons accelerated through a potential difference of 40 kV is approximately 1.31 x 10^-10 meters.
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The wavelength of electrons accelerated from rest through a potential difference of 40 kV is X × 10-12 m. The value of X is _________. (Nearest integer)Given: Mass of electrons = 9.1 × 10-31 kgCharge on an electron = 1.6 × 10-19 CPlancks constant = 6.63 × 10-34 JsCorrect answer is '6'. Can you explain this answer?
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