Tip:
Highlight text to annotate it
X
in this example we are required to find in which energy level of triply ionized beryllium
has the same electron orbital radius as that of ground state of hydrogen. now here in this
situation, as we know that, orbital radii, in any hydrogenic atom can be given as radius
of n-eth orbit is, 0.529 multiplied by n square by z Angstrom.
we can find the radii for any number of orbital using this expression . and in this problem
we are given that . radius of first orbit , of hydrogen that is for ground state , should
be equal to radius of n-ath orbit of beryllium +3.
and we are required to find the value of n- or the energy level of triply ionized beryllium
which has same orbital radius, so in this situation for hydrogen, n equals 1 we know
it is 0.529 angstrom, which is equal to for n-ath orbit in beryllium. as z is equal to,
4 for beryllium. we can substitute here - 0.529, multiplied
by , n square by 4 , here this factor canceled out, we get n square is equal to 4- or the
value of n is 2 , this is the answer to this problem , it means for, beryllium, plus 3.
the radius of second orbit is equal to that of the ground state of hydrogen atom.