Respuesta :
Acceleration is defined as the rate of change of velocity with respect to time.
Formulas of force are given by:
[tex]F=ma[/tex] (1)
where,
F = force
m = mass
a = acceleration
[tex]F=\frac{kq_{1}q_{2}}{r^{2}}[/tex] (2)
where,
F = force
k = coulomb constant ([tex]9\times 10^{9}Nm^{2}C^{-2}[/tex])
r = distance between the charged particles
[tex]q_{1}[/tex] and [tex]q_{2}[/tex] are the signed magnitude of charges
Use the formula (2) for calculating the value of force, we get:
Substitute the value of [tex]q_{1}[/tex] and [tex]q_{2}[/tex], k and r to find the value of force.
F= [tex]\frac{9\times 10^{9} Nm^{2}C^{-2}\times (1.6\times 10^{-19} C)^{2}}{(4.50\times 10^{-10})^{2}}[/tex]
= [tex]1.1378\times 10^{-9} N[/tex]
Now, put the above value force in formula (1) to identify the initial acceleration.
[tex]1.1378\times 10^{-9} N=ma[/tex] (1) (mass of electron =[tex]9.1 \times 10^{-31} kg[/tex])
acceleration of electron = [tex]\frac{1.1378\times 10^{-9} N}{9.1\times 10^{-31}kg}[/tex]
= [tex]1.25\times 10^{21}N/kg[/tex]
And,
acceleration of proton =[tex]\frac{1.1378\times 10^{-9} N}{mass of proton}[/tex]
mass of proton =[tex]1.67 \times 10^{-27}[/tex]
Thus,
acceleration of proton = [tex]\frac{1.1378\times 10^{-9} N}{1.67 \times 10^{-27} kg}[/tex]
=[tex]6.81 \times 10^{17} N/kg[/tex]
Now, initial acceleration of electron and proton is [tex]1.25\times 10^{21}m/s^{2}[/tex] and [tex]6.81 \times 10^{17} m/s^{2}[/tex] as 1 N = [tex]kgm/s^{2}[/tex].
