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If the momentum of an electron is 10 times its rest mass times the speed light, then
- a)its speed is 2.983 x 108 m/s
- b)its speed is 108 m/s
- c)its energy is 9.22 x 10-13 J
- d)its energy is 10-13 J
Correct answer is option 'A,C'. Can you explain this answer?
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Verified Answer
If the momentum of an electron is 10 times its rest mass times the spe...
Given, p = 10 m0c
Using
So,
Solving
and
Putting
we get E = 9.22 x 10-13 J
Using
So,
Solving
and
Putting
we get E = 9.22 x 10-13 J
Most Upvoted Answer
If the momentum of an electron is 10 times its rest mass times the spe...
Explanation:
The momentum of an object is defined as the product of its mass and velocity. In the case of an electron, its momentum can be calculated using the equation:
Momentum (p) = mass (m) x velocity (v)
Given that the momentum of the electron is 10 times its rest mass times the speed of light, we can write this as:
p = 10 x (rest mass of electron) x (speed of light)
Calculating the speed:
To determine the speed of the electron, we need to rearrange the equation for momentum to solve for velocity (v):
p = m x v
v = p/m
Since the rest mass of the electron is a constant value, we can substitute it into the equation:
v = (10 x (rest mass of electron) x (speed of light))/(rest mass of electron)
The rest mass of an electron is approximately 9.11 x 10^(-31) kg, and the speed of light is approximately 3 x 10^8 m/s. Substituting these values into the equation, we get:
v = (10 x 9.11 x 10^(-31) kg x 3 x 10^8 m/s)/(9.11 x 10^(-31) kg) = 30 x 10^8 m/s
Simplifying, we find that the speed of the electron is:
v = 3 x 10^9 m/s = 3 x 10^8 m/s
Therefore, the correct answer is option A: its speed is 2.983 x 10^8 m/s.
Calculating the energy:
The energy of a moving object can be calculated using the equation:
Energy (E) = (1/2) x mass (m) x velocity^2 (v^2)
Substituting the values for mass and velocity into the equation, we get:
E = (1/2) x (rest mass of electron) x (velocity)^2
E = (1/2) x 9.11 x 10^(-31) kg x (3 x 10^8 m/s)^2
Simplifying, we find that the energy of the electron is:
E = (1/2) x 9.11 x 10^(-31) kg x 9 x 10^16 m^2/s^2
E = 4.095 x 10^(-14) J
Therefore, the correct answer is option C: its energy is 9.22 x 10^(-13) J.
The momentum of an object is defined as the product of its mass and velocity. In the case of an electron, its momentum can be calculated using the equation:
Momentum (p) = mass (m) x velocity (v)
Given that the momentum of the electron is 10 times its rest mass times the speed of light, we can write this as:
p = 10 x (rest mass of electron) x (speed of light)
Calculating the speed:
To determine the speed of the electron, we need to rearrange the equation for momentum to solve for velocity (v):
p = m x v
v = p/m
Since the rest mass of the electron is a constant value, we can substitute it into the equation:
v = (10 x (rest mass of electron) x (speed of light))/(rest mass of electron)
The rest mass of an electron is approximately 9.11 x 10^(-31) kg, and the speed of light is approximately 3 x 10^8 m/s. Substituting these values into the equation, we get:
v = (10 x 9.11 x 10^(-31) kg x 3 x 10^8 m/s)/(9.11 x 10^(-31) kg) = 30 x 10^8 m/s
Simplifying, we find that the speed of the electron is:
v = 3 x 10^9 m/s = 3 x 10^8 m/s
Therefore, the correct answer is option A: its speed is 2.983 x 10^8 m/s.
Calculating the energy:
The energy of a moving object can be calculated using the equation:
Energy (E) = (1/2) x mass (m) x velocity^2 (v^2)
Substituting the values for mass and velocity into the equation, we get:
E = (1/2) x (rest mass of electron) x (velocity)^2
E = (1/2) x 9.11 x 10^(-31) kg x (3 x 10^8 m/s)^2
Simplifying, we find that the energy of the electron is:
E = (1/2) x 9.11 x 10^(-31) kg x 9 x 10^16 m^2/s^2
E = 4.095 x 10^(-14) J
Therefore, the correct answer is option C: its energy is 9.22 x 10^(-13) J.
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If the momentum of an electron is 10 times its rest mass times the speed light, thena)its speed is 2.983 x 108 m/sb)its speed is 108 m/sc)its energy is 9.22 x 10-13 Jd)its energy is 10-13 JCorrect answer is option 'A,C'. Can you explain this answer?
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