What is the ratio of speeds of an electron in the first orbit of he^ + ion and 2nd orbit of h-atom?

The ratio of the velocity of the electron in the first orbit to that in the second orbit is ____________.

The ratio of the velocity of the electron in the first orbit to that in the second orbit is 2 : 1.

Explanation:

`"v" prop 1/"n"`

`therefore "v"_1/"v"_2 = "n"_2/"n"_1 = 2/1`

Concept: Bohr’s Atomic Model

Is there an error in this question or solution?

India's Super Teachers for all govt. exams Under One Roof

Enroll For Free Now

CONCEPT:

Bohr's Atomic Model:

Bohr proposed a model for hydrogen atom which is also applicable for some lighter atoms in which a single electron revolves around a stationary nucleus of positive charge Ze (called hydrogen-like atom).

Bohr's model is based on the following postulates:

He postulated that an electron in an atom can move around the nucleus in certain circular stable orbits without emitting radiations.
Bohr found that the magnitude of the electron's angular momentum is quantized i.e.

\(⇒ L = m{v_n}\;{r_n} = n\left( {\frac{h}{{2\pi }}} \right)\)

Where n = 1, 2, 3, ..... each value of n corresponds to a permitted value of the orbit radius, rn = Radius of nth orbit, vn = corresponding speed, and h = Planck's constant

EXPLANATION:

According to Bohr's atomic model, the speed of the electron in the nth orbit is given as,

\(⇒ v_n=2.2\times10^6\frac{Z}{n}\,m/sec\) -----(1)

Where Z = atomic number

For ground-state n = 1,

\(⇒ v_n=2.2\times10^6\times\frac{Z}{1}\,m/sec\)

⇒ vn ∝ Z -----(2)

For H atom, Z = 1

For He+ ion, Z = 2

For Li+2 ion, Z = 3

By equation 2 we can say that the speed of the electron in the ground state is directly proportional to the atomic number.
We know that the atomic number of Li+2 is maximum compared to the H atom and He+ ion.
So the speed of the electron in the ground state is maximum for Li+2 ion. Hence, option 3 is correct.

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free Download App

Trusted by 3.4 Crore+ Students

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Suggest Corrections