An alpha-particle has 2.2 10 –13 J of kinetic energy.What is the speed of the alpha-particle?A 4.1 10 6 m s–1B 5.8 10 6 m s–1C 8.1 10 6 m s–1D 1.2 10 7 m s–1
Question
An alpha-particle has 2.2 10 –13 J of kinetic energy.What is the speed of the alpha-particle?A 4.1 10 6 m s–1B 5.8 10 6 m s–1C 8.1 10 6 m s–1D 1.2 10 7 m s–1
Solution 1
To solve this problem, we need to use the formula for kinetic energy, which is KE = 1/2 mv^2, where m is the mass and v is the velocity.
The mass of an alpha particle is known to be 6.64424 x 10^-27 kg.
Given that the kinetic energy (KE) is 2.2 x 10^-13 J, we can rearrange the formula to solve for v:
v = sqrt((2*KE)/m)
Substituting the given values:
v = sqrt((2*2.2 x 10^-13 J)/(6.64424 x 10^-27 kg))
v = sqrt(6.6 x 10^-14 J/kg)
v = 1.02 x 10^7 m/s
However, this value is not in the options provided. It's possible there was a mistake in the problem or in the provided options. Please check the values again.
Solution 2
To solve this problem, we need to use the formula for kinetic energy, which is KE = 1/2 mv^2, where m is the mass and v is the velocity.
The kinetic energy of the alpha particle is given as 2.2 x 10^-13 J.
The mass of an alpha particle is known to be 6.644 x 10^-27 kg.
We can rearrange the formula to solve for v: v = sqrt((2*KE)/m).
Substituting the given values into the formula, we get:
v = sqrt((2*2.2 x 10^-13 J)/(6.644 x 10^-27 kg))
Solving this will give us the speed of the alpha particle.
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