Answer:
the velocity of the gold nuclei
the angle of the velocity of gold nuclei = 29.64° clockwise (i.e down the horizontal)
the final kinetic energy of helium nucleus is
Explanation:
The formula for kinetic Energy (K.E) is:
where;
= mass of the helium
= velocity of helium
replacing and
; we have :
Applying conservation of momentum along x- axis since the collision is elastic
------ equation (1)
where
= mass of helium and gold respectively
= initial velocity of helium
= final velocity of gold
= scattered angle for helium and gold respectively
Along the y - axis; the equation for conservation of momentum is :
---- equation (2)
Equating equation (1) and (2); we have:
----- equation (3)
However, the conservation of internal kinetic energy guves:
Making the subject of the formula ; we have:
----- equation (4)
Replacing the expression of in equation (3) into equation (4) ; we have
In the above expression;
replacing ;
;
;
;
; we have:
The above is a quadratic equation; now solving by using the quadratic formula; we have:
since we are considering the positive value from the above expression; we have
NOW; we substitute our known values into equation (4) in order to solve for ; we have:
Therefore; the velocity of the gold nuclei
From equation (2)
Therefore replacing our known values and solving for ; we have:
∴ the angle of the velocity of gold nuclei = 29.64° clockwise (i.e down the horizontal)
b) Equation to determine the final kinetic energy of helium is:
=
Thus, the final kinetic energy of helium nucleus is
I hope this explanation helps alot!.