Question

In: Chemistry

Calculate the probability of finding an electron in a 1s orbital outside of the first Bohr...

Calculate the probability of finding an electron in a 1s orbital outside of the first Bohr orbit (a0).

Expert Solution

The eigenfunction for a 1s electron of a hydrogen-like atom is given by the following expression

where k is a constant,

a_o is the radius of the first Bohr orbit for hydrogen.

The radius at which there is a maximum probability of finding a 1s electron (in any direction) is just

.

The probability of finding an electron in unit element of volume at distance r is given by . And the probability of finding the electron at distance r, irrespective of direction, is given by

,

And if we know that:

then the above expression can be written as

, where is a constant.

Now, all you have to do is use the value of the radius and Ao, along with k2 to calculate this. Those data you are not providing that, but it does not matter. You already have the expression to calculate this.

Hope this helps

queen_honey_blossom answered 2 years ago

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