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Two electrons are moving with speeds v1 = √ 3c 2 and v2 = c/2 respectively. The ratio of de-Broglie wavelength of first electron to that of second electron is —— (answer must be an integer)?
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Two electrons are moving with speeds v1 = √ 3c 2 and v2 = c/2 respecti...
Given:
- Speed of first electron (v1) = √3c^2
- Speed of second electron (v2) = c/2
To find:
Ratio of de-Broglie wavelength of first electron to that of second electron
Solution:
1. De-Broglie wavelength:
De-Broglie wavelength (λ) is given by the equation: λ = h/p
where,
- λ is the de-Broglie wavelength
- h is the Planck's constant (h = 6.626 x 10^-34 J.s)
- p is the momentum of the particle
2. Momentum of the electron:
Momentum (p) of a particle is given by the equation: p = mv
where,
- p is the momentum
- m is the mass of the particle
- v is the velocity of the particle
3. Calculation of momentum:
The mass of an electron (m) is a constant value.
Momentum of first electron (p1) = m * v1
Momentum of second electron (p2) = m * v2
4. Calculation of de-Broglie wavelength:
De-Broglie wavelength of first electron (λ1) = h / p1
De-Broglie wavelength of second electron (λ2) = h / p2
5. Calculation of ratio:
Ratio of de-Broglie wavelength of first electron to that of second electron:
Ratio = λ1 / λ2
= (h / p1) / (h / p2)
= (p2 / p1)
6. Substituting values:
p1 = m * v1
p2 = m * v2
Ratio = (m * v2) / (m * v1)
= (v2 / v1)
7. Substituting given values:
v1 = √3c^2
v2 = c/2
Ratio = (c/2) / (√3c^2)
= (c/2) * (1 / √3c)
= 1 / (2√3)
= 1 / (2√3) * (√3 / √3)
= √3 / 6
Therefore, the ratio of de-Broglie wavelength of the first electron to that of the second electron is √3 / 6.
- Speed of first electron (v1) = √3c^2
- Speed of second electron (v2) = c/2
To find:
Ratio of de-Broglie wavelength of first electron to that of second electron
Solution:
1. De-Broglie wavelength:
De-Broglie wavelength (λ) is given by the equation: λ = h/p
where,
- λ is the de-Broglie wavelength
- h is the Planck's constant (h = 6.626 x 10^-34 J.s)
- p is the momentum of the particle
2. Momentum of the electron:
Momentum (p) of a particle is given by the equation: p = mv
where,
- p is the momentum
- m is the mass of the particle
- v is the velocity of the particle
3. Calculation of momentum:
The mass of an electron (m) is a constant value.
Momentum of first electron (p1) = m * v1
Momentum of second electron (p2) = m * v2
4. Calculation of de-Broglie wavelength:
De-Broglie wavelength of first electron (λ1) = h / p1
De-Broglie wavelength of second electron (λ2) = h / p2
5. Calculation of ratio:
Ratio of de-Broglie wavelength of first electron to that of second electron:
Ratio = λ1 / λ2
= (h / p1) / (h / p2)
= (p2 / p1)
6. Substituting values:
p1 = m * v1
p2 = m * v2
Ratio = (m * v2) / (m * v1)
= (v2 / v1)
7. Substituting given values:
v1 = √3c^2
v2 = c/2
Ratio = (c/2) / (√3c^2)
= (c/2) * (1 / √3c)
= 1 / (2√3)
= 1 / (2√3) * (√3 / √3)
= √3 / 6
Therefore, the ratio of de-Broglie wavelength of the first electron to that of the second electron is √3 / 6.
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Two electrons are moving with speeds v1 = √ 3c 2 and v2 = c/2 respectively. The ratio of de-Broglie wavelength of first electron to that of second electron is —— (answer must be an integer)?
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