Question

Which of the following products in a hydrogen atom are independent of the principal quantum number n? The symbols have their usual meanings.
(a) vn
(b) Er
(c) En
(d) vr

Answer 1

Answer:

option b)Er.......... Hope this will helpful for you

Answer 2

The particles that are independent of the principle quantum number n are a) vn b) Er

Explanation:

• In general we know that the velocity of the electron is given as  $v a \frac{z}{n}$ so,$v n \alpha Z$
• From the above derivation we can clearly see that “vn” is directly proportional to the quantum number and hence option a) can be accepted as a a particle that is not dependent on the principal quantum number “n”,

• Also we know that Er can be related to Z as follows,

        $E \alpha \frac{z^{2}}{n^{2}}$

        where

        $r \alpha \frac{n^{2}}{Z}$

       And hence finally we can conclude that,

       $\text { Er } \alpha Z$

• From the above derivation we can clearly see that Er is also directly proportional to Z and Hence we can conclude that Er and Vn both are Independent of the principle quantum number “n”.