The \"size\" of the atom in Rutherford\'s model is about 1.0 10 10 m. (a) Determ

Question

The "size" of the atom in Rutherford's model is about 1.0 1010 m.

(a) Determine the speed of an electron moving about the proton using the attractive electrostatic force between an electron and a proton separated by this distance.
m/s

(b) Does this speed suggest that Einsteinian relativity must be considered in studying the atom?

Yes

No    

(c) Compute the de Broglie wavelength of the electron as it moves about the proton.
nm

(d) Does this wavelength suggest that wave effects, such as diffraction and interference, must be considered in studying the atom?

Yes

No   

Explanation / Answer

part a:

mass of electron=me=9.1*10^(-31) kg

mass of proton=mp=1.67*10^(-27) kg

charge on electron=-e=-1.6*10^(-19) C

charge on proton=e=1.6*10^(-19) C

let speed of electron is v m/s

then the attractive force between two opposing charges of electron and proton

is balanced by centripetal force.

hence k*(e)*e/r^2=me*v^2/r

where k=9*10^9 F/m

then v^2=k*e^2/(r*me)

==>v=sqrt(k*e^2/(r*me))

=1.5911*10^6 m/s

part b:

speed found in part a=5.3*10^(-3)*c

where c=speed of light=3*10^8 m/s

hence einstein relativity is not required to be considered as speed is very less than speed of light

c)de broglie wavelength=plank's constant/momentum

=h/(me*v)

=6.626*10^(-34)/(9.1*10^(-31)*1.5911*10^6)=4.576*10^(-10) m

d) as wavelength is of the same order as of size of the radius

wave efeects should be considered in studying the atom

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.