An electron at ground state in the atom (-10.38eV)is struck by a passing electron with 7.00eV of energy. What is the velocity of the passing electron afrer the collision?
To find the velocity of the passing electron after the collision, we need to apply the principle of conservation of energy and momentum. This principle states that the total energy and momentum before the collision is equal to the total energy and momentum after the collision.
First, let's calculate the momentum of the passing electron before the collision. The momentum of an object can be calculated using the formula:
p = mv
Where p is the momentum, m is the mass, and v is the velocity.
We don't have the mass of the electron, but we can use its energy to find the velocity using the equation:
E = (1/2)mv^2
Rearranging the equation, we have:
v = sqrt(2E/m)
Using the energy given E = 7.00 eV and the mass of an electron m = 9.10938356 × 10^-31 kg, we can calculate the velocity. However, we need to convert the energy from electron-volts (eV) to joules (J) since the mass is given in kilograms.
To convert from eV to J, we use the following conversion factor:
1 eV = 1.602176634 × 10^-19 J
Thus, 7.00 eV is equivalent to:
7.00 eV * (1.602176634 × 10^-19 J / 1 eV) = 1.12252364 × 10^-18 J
Now, let's calculate the velocity using the formula:
v = sqrt(2E/m) = sqrt(2 * 1.12252364 × 10^-18 J / 9.10938356 × 10^-31 kg)
After performing the calculation, we find that the velocity of the passing electron after the collision is approximately 6.60 × 10^6 m/s.