A Mysterion Affair

Chemistry Level 4

Suppose that we have a hydrogen atom. If we take its one electron and replace it with another particle (let us call it the $Mysterion$ ) that carries the same charge but has double the mass of the original electron, which of the following are true? {assume that the existence of such a particle is purely for the sake of the question}

(1) The speed of the $Mysterion$ in a shell will be equal to the speed of the electron that was in the same shell.
(2) The radius of the 3rd orbit will be same for both the electron as well the $Mysterion$ .
(3) Energy gap between the levels of the hydrogen atom will not change.
(4) The ionization energy of the atom, needed to remove the $Mysterion$ will not change.

What is the sum of the correct option numbers?

Eg. If the answer is 2 and 3, input your answer as 5.

The answer is 1.

1 solution

Jay Steller
Mar 12, 2017

Solution:

Velocity of a particle in orbit is given by: $2πkzE^2/nh$ This is independent of the mass of the particle, so the $Mysterion$ will have the same velocity as the electron.
Radius of orbit is given by $n^2h^2/4π^2kzE^2m$ Since this has a term $m$ representing mass, it will change. Thus radius of the 3rd orbit differs for the $Mysterion$ and the electron.
Total Energy is given by $-2π^2K^2z^2E^4m/n^2h^2$ So both ionization energy and energy gap will change.

Thus only the first option is correct.

A Mysterion Affair

The answer is 1.

1 solution

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