A certain moving electron has a kinetic energy
of 1.01 × 10−19 J.
Calculate the speed necessary for the electron to have this energy. The mass of an
electron is 9.109 × 10−31 kg.
Answer in units of m/s.
To calculate the speed necessary for the electron to have a kinetic energy of 1.01 × 10^-19 J, we can use the formula for kinetic energy:
KE = (1/2)mv^2
Where:
KE is the kinetic energy,
m is the mass of the electron, and
v is the velocity or speed of the electron.
We can rearrange the formula to solve for v:
v = √((2KE) / m)
Now we can substitute the given values into the formula:
KE = 1.01 × 10^-19 J
m = 9.109 × 10^-31 kg
v = √((2 * 1.01 × 10^-19 J) / 9.109 × 10^-31 kg)
To simplify the calculation, we can convert the given joules (J) to electron volts (eV):
1 eV = 1.6 × 10^-19 J
So, 1.01 × 10^-19 J = (1.01 × 10^-19 J) / (1.6 × 10^-19 J/eV) ≈ 0.63 eV
Now we can substitute the calculated value:
v = √((2 * 0.63 eV) / 9.109 × 10^-31 kg)
To further simplify the calculation, we can convert electron volts (eV) to joules (J) by multiplying by 1.6 × 10^-19 J/eV:
0.63 eV = (0.63 eV) * (1.6 × 10^-19 J/eV) ≈ 1.01 × 10^-19 J
Now we have:
v = √((2 * 1.01 × 10^-19 J) / 9.109 × 10^-31 kg)
Calculating the expression:
v ≈ √(2.22 × 10^11 m^2/s^2)
Taking the square root:
v ≈ 4.71 × 10^5 m/s
Therefore, the speed necessary for the electron to have a kinetic energy of 1.01 × 10^-19 J is approximately 4.71 × 10^5 m/s.
To calculate the speed necessary for the electron to have the given kinetic energy, we can use the equation for kinetic energy:
KE = (1/2) * m * v^2
Where:
KE is the kinetic energy
m is the mass of the electron
v is the velocity (speed) of the electron
We can rearrange this equation to solve for v:
v^2 = (2 * KE) / m
Let's substitute the given values into the equation:
KE = 1.01 × 10^(-19) J
m = 9.109 × 10^(-31) kg
v^2 = (2 * 1.01 × 10^(-19) J) / (9.109 × 10^(-31) kg)
Now we can calculate v by taking the square root of both sides of the equation:
v = sqrt((2 * 1.01 × 10^(-19) J) / (9.109 × 10^(-31) kg))
Performing the calculation gives us:
v ≈ 5.93 × 10^6 m/s
Therefore, the speed necessary for the electron to have this energy is approximately 5.93 × 10^6 m/s.
Since the kinetic energy is
KE = (1/2)mV^2,
The speed is V = sqrt(2*KE/m)
They have told you the values of KE and m; so do the calculation.