In this illustration, we'll be, discussing
about accelerated electrons, which collide
with hydrogen atom. here we are given that
electrons are emitted from an electron gun
at almost zero velocity and are accelerated
by an electric field through a distance of
1 meter. so they gain kinetic energy due to
work done by electric field. here, the electrons
are now scattered by an atomic hydrogen sample
in ground state. it is asking what should
be the minimum value of electric field so
that red light of wavelength 6 5 6 3 angstrom.
may be emitted, in the hydrogen. now in this
solution here we can write. first we calculate.
the energy of, red light emitted. in hydrogen
gas is. this energy we can write, 1 2 4 3
1 divided by. 6 5 6 3. and this gives us direct
energy in electron volt numerically it is
1 point, 8 9 electron volt. and 1 point 8
9 you know this corresponds to. transition
from. n 2 equal to 3 to, n 1 equal to 2. that
means if, hydrogen atom is making a transition
from 3 to 2. this implies, hydrogen must be
first excited 2 n equal to 3 then only this
radiation can be emitted. so here we can write
thus. for it. hydrogen atom. must be excited.
to n equal to 3 state. which requires. energy.
delta e is equal to which we can write, e
3 minus, e 1. and we know the numerical values.
the energy of, third orbit is, taken as minus
1 point 5 1 electron volt minus of the first
1 is minus. 13 point 6 electron volt which
gives us. 12 point 0 9 electron volt this
is the energy which is required. now, this
much amount of energy is to be supplied 2
hydrogen atom by collision of these accelerated
electrons. so that this will first excite
from n equal to 1 to 3 and then, during d-excitation
it can emit this red light. so here, we can
use this implies. the energy of. accelerated
electrons, should be. this energy, we can
write 12 point is zero 9 electron volt and
it should be equal to. q e multiplied by the
distance to which these are accelerated. so
here numerically on solving we get the value
of electric field which is 12 point, zero
9. multiplied by 1 point 6 into 10 to power
minus 19. divided by q d. and the value of
q is again 1 point 6 into 10 to power minus
19 and b is given here as 1 meter. so solving
this we get it 12 point, 0 9 volt per meter
that should be the result of this problem.
the minimum required value of electric field
for which this red light can be emitted.
