The Bohr Model of the hydrogen atom proposed that there were very specific energ

Question

The Bohr Model of the hydrogen atom proposed that there were very specific energy states that the electron could be in. These states were called stationary orbits or stationary states. Higher energy states were 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 n is a positive integer representing the shell or orbit.

a.) What is the radius of the n=2 orbit for Hydrogen (Z=1)? Tries 0/10

Each shell 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 all shells in which the electron is bound in orbit around the nucleus.

b.) What is the energy for the n=2 Bohr orbit for Hydrogen (Z=1) expressed in Joules? (do not enter units) Tries 0/10

c.) What is the energy for the n=2 Bohr orbit for Hydrogen (Z=1) expressed in eV? (do not enter units) Tries 0/10

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, Li+2, Be+3, ....

d.) What is the radius of the n=4 Bohr orbit for B+4 (Boron, Z=5)? Tries 0/10

e.)What is the energy of the n=4 Bohr orbit for Be+3 (Beryllium, Z=4)? You can use your choice of energy units. Make sure to enter units this time.

Explanation / Answer

a.) For hydrogen, the radius of the nth orbit is given by:

r = (n2a0)/Z,

where, a0 = Bohr radius = 5.29177x10 -11m

Here, we have Z = 1 for hydrogen atoms and we have to find the radius of the n=2 orbit for Hydrogen. So we have:

r = (n2a0)/Z = [4X(5.29177x10 -11m)]/1 = 21.16x10 -11m

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c) The energy for nth orbit for Hydrogen atom is given by;

En = -(13.6eV)/n2

So, energy for the n=2 Bohr orbit for Hydrogen is given by:

E2 =  -(13.6eV)/(2)2 = -3.4eV

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b) We saw in (c) that energy for the n=2 Bohr orbit for Hydrogen is given by:

E2 = -3.4eV

Now 1eV = 1.6X10-19J

So E2 = -3.4eV = -3.4(1.6X10-19J) = -5.44X10-19J

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d.) For hydrogen like ions, the radius of the nth orbit is given by:

r = (n2a0)/Z

Here Z = 5, n = 4, So radius of the n=4 Bohr orbit for B+4 is given by:

r = (n2a0)/Z = [(4)2(5.29177x10 -11m)]/5 = 16.93x10 -11m

This concludes the answers. Check the answer and let me know if it's correct. If you need anymore clarification or correction I will be happy to oblige....

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