You have large sample of Hydrogen atoms. A bunch of the atoms have their electro

Question

You have large sample of Hydrogen atoms. A bunch of the atoms have their electron in the n = 2, l = 0
state, and a bunch of the atoms have their electron in the n = 1, l = 0 state. For each of these atoms, you
will make a measurement of the location of the electron’s position within the atom.
What will you find when you make these measurements?

a. the electrons for the n = 2 state will always be found at the same distance from the nucleus, and this
distance will be half the distance of the electrons in the n = 1 state.
b. the electrons for the n = 2 state will always be found at the same distance from the nucleus, and this
distance will be four times greater than the distance for the electrons in the n = 1 state.
c. in both cases, the electrons will be found at a range of distances from the nucleus, but the most common
location for the n = 2 state will be about half the most common location for the n = 1 state.
d. in both cases, the electrons will be found at a range of distances from the nucleus, but the most common
location for the n = 2 state will be about four times greater than the most common location for the n =1
state.
e. in both cases, the electrons will be found at range of distances from the nucleus, but it is impossible to
predict anything about how the measured locations will compare.

Explanation / Answer

According to Bohr's radius

for n=1

r_1   = 0.0529nm

r_n   = 0.0529*n^2 nm

r_2 = (0.0529) *(2)^2 nm

r_2 = 4*0.0529 nm = 4*r_1

answer ; (b)

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