A proton collides head on with a helium atom at rest. Their combined velocity after the collision is 8 x 10^5 ms^-1. Calculate the initial velocity of the proton.
*** HELP PO PLEASE!!
You seem to be describing an inelastic collision in which the helium and hydrogen atoms stick together to form a helium hydride molecule. If so, use the law of conservation of momentum.
Apparently your teacher or text book writer is unaware that there is no such thing as an HeH molecule.
then what can be the answer to this problem sir/maam?
The final "combined" velocity would be 1/5 of the initial velocity of the proton.
Ignore my previous comment about HeH. What you would be forming is the ion HeH+. Apparently they do exist.
To solve this problem, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum: In an isolated system, the total momentum before the collision is equal to the total momentum after the collision.
Initial momentum of the system = Final momentum of the system
Let's assign variables to the initial and final velocities of the proton and the helium atom.
- Initial velocity of the proton: v_proton_initial
- Initial velocity of the helium atom: v_helium_initial
- Final velocity of the system after the collision: v_final
Therefore, the equation for conservation of momentum can be written as:
(Mass of proton x v_proton_initial) + (Mass of helium atom x v_helium_initial) = (Mass of proton + mass of helium atom) x v_final
2. Conservation of kinetic energy: In an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Initial kinetic energy of the system = Final kinetic energy of the system
The kinetic energy of an object can be calculated using the formula: KE = 0.5 x mass x velocity^2
The total initial kinetic energy of the system can be written as:
[(0.5 x proton mass x v_proton_initial^2) + (0.5 x helium mass x v_helium_initial^2)]
And the total final kinetic energy of the system after the collision is:
[(0.5 x proton mass x v_final^2) + (0.5 x helium mass x v_final^2)]
Now, we can solve the equations simultaneously to find the initial velocity of the proton.
Let's assume:
- Mass of proton (Mp) = 1.67 x 10^-27 kg
- Mass of helium atom (Mh) = 6.64 x 10^-27 kg
- Final velocity of the system (v_final) = 8 x 10^5 m/s
Plug in these values into the equations and solve for v_proton_initial.
(Mp x v_proton_initial) + (Mh x 0) = (Mp + Mh) x v_final [Since the helium atom is initially at rest]
v_proton_initial = [(Mp + Mh) x v_final] / Mp
Substitute the given values into the equation and calculate v_proton_initial.