Question

the velocity of orbital motion of an electron in an atom varies with the atomic number Z as​

Answer 1

Answer:

which class question is this

Answer 2

Answer:

Velocity varies as inversely proportional to atomic number (Z).

Concept:

Bohr's Theory was quite effective at introducing new ideas about atoms. The relationship proposed by Bohr is similar to the empirical relationship proposed on the spectral lines in the spectra of H-atoms, Balmer and Rydberg. The value of R as determined by Bohr's theory is identical to that determined by the empirical relationship.

So, from the second postulate of Bohr's, we get :

$mv_{n} r_{n} = \frac{nh}{2\pi }$ ...(1)

First we will solve for radius from equation(1).

$r_{n} = \frac{n^{2}h^{2} }{4\pi ^{2} Kme^{2}Z } \\r_{n} = \frac{0.53 n^{2} }{ZA}$

Now, we solve for velocity from equation(1).

$v_{n} = \frac{2\pi ^{2} Kme^{2}Z }{nh}$

The orbital velocity of an electron varies directly with atomic number for a given orbit (n = constant) ($v_{n}\propto Z$).

The orbital velocity of the electron varies inversely with orbit order for a specific element (Z=constant).

So, the velocity of orbital motion of an electron in an atom varies with the atomic number Z as​ inversely proportional.

#SPJ2