1) First of all, let's calculate the potential difference between the initial point (infinite) and the final point (d=0.529x10-10 m) of the electron.
This is given by:
Where E is the electric field generated by the proton, which is
where
is the Coulomb constant and
is the proton charge.
Replacing the electric field formula inside the integral, we obtain
2) Then, we can calculate the work done by the electric field to move the electron (charge
) through this
. The work is given by
There are a lot.
Some of them are
Gamma radiation
X-ray radiation
Ultraviolet radiation
Visible radiation
Infrared radiation
Microwave radiation
The impulse is equal to the variation of momentum of the object:
where m is the mass object and
is the variation of velocity of the object.
The ball starts from rest so its initial velocity is zero:
. So we can rewrite the formula as
or
and since we know the impulse given to the ball (I=16 Ns) and its mass (m=2 kg), we can find the final velocity of the ball:
a.) K 2=K 1 +GmM( r 21− r 11)=2.2×10 7J
b.) K 2 +GmM( r 11− r 21)=6.9×10 7 J
Applying Law of Energy conservation :
K 1+U 1
=K 2+U 2
⇒K 1− r 1GmM
=K 2− r 2 GmM
where M=5.0×10 23kg,r1
=> R=3.0×10 6m and m=10kg
(a) If K 1
=5.0×10 7J and r 2
=4.0×10 6 m, then the above equation leads to
K 2=K 1 +GmM (r 21− r 11)=2.2×10 7J
(b) In this case, we require K 2
=0 and r2
=8.0×10 6m, and solve for K 1:K 1
=K 2 +GmM (r 11− r 21)=6.9×10 7 J
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A and c should be the answer
