Complete Question:
A deuteron (a nucleus that consists of one proton and one neutron) is accelerated through a 4.01 kV potential difference. b) How much kinetic energy does it gain? The mass of a proton is 1.67262 × 10−27 kg, the mass of a neutron 1.67493 × 10−27 kg and the charge on an electron −1.60218 × 10−19 C. Answer in units of J\
b) what is the speed?
Answer:
a) the kinetic energy gained = 6.42 * 10⁻¹⁶ J
b) the speed of the particle, v = 619328.3 m/s
Step-by-step explanation:
q = 1.602 *10⁻¹⁹C
V = 4.01 kV = 4.01 * 10³ V
Work done by the deuteron = qV
Work done by the deuteron = 1.602 * 10⁻¹⁹ * 4.01 *10³
Work done = 6.42 * 10⁻¹⁶ J
Kinetic Energy gained = work done
Kinetic Energy gained by the deuteron = 6.42 * 10⁻¹⁶ J
B) The formula for Kinetic Energy is given by:
KE = 1/2 Mv²
Let the mass of the proton be m₁ = 1.67262 × 10⁻²⁷kg
Let the mass of the neutron be m₂ = 1.67493 × 10−27 kg
M = m₁ + m₂
KE = 1/2 ( m₁ + m₂)v²
Let v = speed of the deuteron
From part (a)
KE = 6.42 * 10⁻¹⁶ J
1/2 ( m₁ + m₂)v²= 6.42 * 10⁻¹⁶
0.5 * (1.67262 + 1.6749) *10⁻²⁷ * v² = 6.42 * 10⁻¹⁶
v = 619328.3 m/s