The Bohr Model of the hydrogen atom proposed that there were very specie energy

Question

The Bohr Model of the hydrogen atom proposed that there were very specie energy states that the electron could Be in. These states were called stationary orbits or stationary states. Higher energy Hates nr-r further from the nucleus. These orbits were thought to be essentially spherical shells in which the electrons orbited at a fixed radius or distance from the nucleus The smallest orbit Is represented by n=1, the next smallest n=2, and so on, where ns a positive integer representing the shell or orbit. What is the radius of the n-5 orbit for Hydrogen (Z=1)? each shall has a very specific energy Note that the energy of zero is used to represent the level at which an electron becomes unbound from the nucleus and can fly free. The energies for the Bohr orbits are all negative, which means they are an she Is in which the electron is bound in orbit around the nucleus. What is the energy for the n=2 Bohr orbit for Hydrogen (Z=1) expressed in Joules' (do not enter units) What is the energy for the n=2 Bohr orbit for Hydrogen (Z=1) expressed in eV? (do not enter units) The Bohr Model does a good Job of calculating the energy levels for ions that are hydrogen like, meaning they may have more protons in the nucleus. But they only have one electron. Examples would be He^+1, U^+2, Be^+3, .... What is the radius of the n=5 Bohr orbit for He^+1 (Helium, Z=2)? What is the energy of the n=2 Bohr orbit for Be^+3 (Beryllium. Z=4)? You can use your choice energy units. Make sum to enter units this time.

Explanation / Answer

a)
radius of nth orbit,

rn = 0.0529*n^2/z nm

n = 5,

r5 = 0.0529*5^2/1 nm

= 1.32 nm or 1.32*10^-9 m

b) Energy of nth state

En = -13.6*z^2 eV/n^2

E2 = -13.6 eV/2^2

= -3.4 eV

= -3.4*1.6*10^-19 J

= -5.44*10^-19 J

c) E2 = -3.4 eV

d)

rn = 0.0529*n^2/z nm

n = 5, z = 2

r5 = 0.0529*5^2/2 nm

= 0.66 nm or 0.66*10^-9 m

e)

Energy of nth state

En = -13.6*z^2 eV/n^2

= -13.6*4^2/2^2

= -54.4 eV

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