Advertisements
Advertisements
Question
What is distance of closest approach?
Solution
The minimum distance between the centre of the nucleus and the alpha particle just before it gets reflected back through 180° is defined as the distance of the closest approach r0 (also known as contact distance).
At this distance, all the kinetic energy of the alpha particle will be converted into electrostatic potential energy
`1/2 mv_0^2 = 1/(4 pi epsilon_0) ((2e)(Ze))/r_0`
⇒ `r_0 = 1/(4 pi epsilon_0) (2Ze^2)/(1/2 mv_0^2)`
= `1/(4 pi epsilon_0) (2Ze^2)/E_k`
where Ek is the kinetic energy of the alpha particle.This is used to estimate the size of the nucleus, but the size of the nucleus is always lesser than the distance of the closest approach.
APPEARS IN
RELATED QUESTIONS
According to the Bohr Theory, which of the following transitions in the hydrogen atom will give rise to the least energetic photon?
In J.J. Thomson e/m experiment, a beam of electron is replaced by that of muons (particle with same charge as that of electrons but mass 208 times that of electrons). No deflection condition is achieved only if
The ratio of the wavelengths for the transition from n =2 to n = 1 in Li++, He+ and H is ______.
The electric potential between a proton and an electron is given by V = V0 In `("r"/"r"_0)`, where r0 is a constant. Assume that Bohr atom model is applicable to potential, then a variation of radius of nth orbit rn with the principal quantum number n is
What is meant by excitation energy?
Write down the draw backs of the Bohr atom model.
Define impact parameter.
Discuss the spectral series of hydrogen atom.
In the Bohr atom model, the frequency of transitions is given by the following expression
v = `"Rc" (1/"n"^2 - 1/"m"^2)`, where n < m
Consider the following transitions:
| Transitions | m → n |
| 1 | 3 → 2 |
| 2 | 2 → 1 |
| 3 | 3 → 1 |
Show that the frequency of these transitions obey sum rule (which is known as Ritz combination principle).
- A hydrogen atom is excited by radiation of wavelength 97.5 nm. Find the principal quantum number of the excited state.
- Show that the total number of lines in emission spectrum is `("n"("n - 1"))/2`.
Compute the total number of possible lines in emission spectrum as given in(a).
