a proton (mass 1.67 x 10^-27 kg) with a velocity of 1.10 x 10 7 m/s collides with a motionless helium nucleus, and the proton bounces back with a speed of 6.00 x 10 6 m/s. The helium nucleus moves forward with a velocity of 4.00 x 10 6 m/s after the bombardment. What is the mass of the helium atom?
momentum is conserved.
initialmomentum=final momentum
mHe*vhe + mp*Vp=mpVp' + mhe*vhe'
solve for mhe.
forward velocity is +, back velocity is -
happy calculating
To find the mass of the helium atom, we need to use the principle of conservation of momentum.
1. The momentum before the collision is equal to the momentum after the collision.
2. Momentum is defined as the product of mass and velocity.
Before the collision:
The momentum of the proton is given by p1 = (mass of proton) x (velocity of proton).
So, p1 = (1.67 x 10^-27 kg) x (1.10 x 10^7 m/s).
Since the helium nucleus is motionless, its momentum is zero (p2 = 0).
After the collision:
The momentum of the proton is given by p3 = (mass of proton) x (final velocity of proton).
So, p3 = (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s).
The momentum of the helium nucleus is given by p4 = (mass of helium atom) x (final velocity of helium nucleus).
So, p4 = (mass of helium atom) x (4.00 x 10^6 m/s).
According to the conservation of momentum, the sum of the momentum before the collision (p1 + p2) is equal to the sum of the momentum after the collision (p3 + p4).
Mathematically, this can be written as:
p1 + p2 = p3 + p4
Plugging in the values, we have:
(1.67 x 10^-27 kg) x (1.10 x 10^7 m/s) + 0 = (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s) + (mass of helium atom) x (4.00 x 10^6 m/s)
Now, we can solve for the mass of the helium atom:
(1.67 x 10^-27 kg) x (1.10 x 10^7 m/s) = (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s) + (mass of helium atom) x (4.00 x 10^6 m/s)
Rearranging the equation to solve for the mass of the helium atom:
(mass of helium atom) x (4.00 x 10^6 m/s) = (1.67 x 10^-27 kg) x (1.10 x 10^7 m/s) - (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s)
Now we can plug in the known values and calculate the mass of the helium atom:
(mass of helium atom) x (4.00 x 10^6 m/s) = (1.67 x 10^-27 kg) x (1.10 x 10^7 m/s) - (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s)
Simplifying the equation:
mass of helium atom = [(1.67 x 10^-27 kg) x (1.10 x 10^7 m/s) - (1.67 x 10^-27 kg) x (6.00 x 10^6 m/s)] / (4.00 x 10^6 m/s)
To find the mass of the helium atom, we need to determine the mass of the helium nucleus and then add the mass of the electrons orbiting around it.
Let's start by finding the mass of the helium nucleus. Given that the proton, with a mass of 1.67 x 10^-27 kg, collides with a motionless helium nucleus, we can use the principle of conservation of momentum to solve the problem.
The momentum before the collision is given by the product of mass and velocity:
momentum_before = mass_proton * velocity_proton = (1.67 x 10^-27 kg) * (1.10 x 10^7 m/s)
The momentum after the collision is given by:
momentum_after = mass_proton * velocity_proton + mass_helium * velocity_helium
Since the helium nucleus is initially at rest and moves forward with a velocity of 4.00 x 10^6 m/s after the collision, we can write the equation as:
momentum_after = (1.67 x 10^-27 kg) * (-6.00 x 10^6 m/s) + (mass_helium) * (4.00 x 10^6 m/s)
Using the conservation of momentum, we can set momentum_before equal to momentum_after:
(1.67 x 10^-27 kg) * (1.10 x 10^7 m/s) = (1.67 x 10^-27 kg) * (-6.00 x 10^6 m/s) + (mass_helium) * (4.00 x 10^6 m/s)
Now, we can solve for mass_helium:
mass_helium = [(1.67 x 10^-27 kg) * (1.10 x 10^7 m/s) - (1.67 x 10^-27 kg) * (-6.00 x 10^6 m/s)] / (4.00 x 10^6 m/s)
Calculating this equation, we obtain:
mass_helium ≈ 6.675 x 10^-27 kg
Therefore, the mass of the helium atom is approximately 6.675 x 10^-27 kg.