Final answer:
The velocity of the electrons at an energy of 1.12 × 10⁻¹⁴ J is 1.62 × 10³ m/s.
Step-by-step explanation:
The velocity of the electrons can be calculated using the formula:
velocity = sqrt((2 * energy) / (mass * c^2))
where energy is the given value of 1.12 × 10⁻¹⁴ J and c is the speed of light, approximately 3 × 10^8 m/s. The mass of an electron is approximately 9.11 × 10⁻³¹ kg.
Substituting the values, the velocity of the electrons is calculated as:
velocity = sqrt((2 * 1.12 × 10⁻¹⁴ J) / (9.11 × 10⁻³¹ kg * (3 × 10^8 m/s)^2))
velocity = 1.62 × 10³ m/s