A stationary proton absorbs an x-ray with a wavelength of 0.24 nm. Determine the proton's final velocity.
momentum of photon = h/wavelength ---> m*v of proton
To determine the proton's final velocity, we need to use the principle of conservation of momentum.
The momentum of an object is given by the equation:
p = m * v
Where p is the momentum, m is the mass, and v is the velocity.
Initially, the proton is stationary, so its initial momentum is zero. After absorbing the x-ray, the proton will acquire some velocity, and we need to find that velocity.
The momentum of the x-ray can be calculated using the equation:
p_x-ray = h / λ
Where p_x-ray is the momentum of the x-ray, h is the Planck's constant (6.626 x 10^-34 J·s), and λ is the wavelength of the x-ray.
Substituting the values, we can calculate the momentum of the x-ray:
p_x-ray = (6.626 x 10^-34 J·s) / (0.24 x 10^-9 m)
Now, the total momentum after the collision should be conserved. Since the initial momentum of the proton is zero, the final momentum will be equal to the momentum of the x-ray:
p_final = p_x-ray
Now we can find the final velocity of the proton by rearranging the momentum equation:
p_final = m * v_final
Solving for v_final:
v_final = p_final / m
Substituting the values we have:
v_final = (6.626 x 10^-34 J·s) / (0.24 x 10^-9 m * mass of proton)
The mass of a proton is approximately 1.67 x 10^-27 kg. Substituting this value into the equation, we get:
v_final = (6.626 x 10^-34 J·s) / (0.24 x 10^-9 m * 1.67 x 10^-27 kg)
Calculating this expression will give us the final velocity of the proton after absorbing the x-ray.