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
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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.
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