Options

A. P-2,Q-1,R-4,S-3
B. P-1,Q-3,R-2,S-4
C. P-2,Q-4,R-1,S-3
D. P-4,Q-1,R-2,S-3

Answer

C

Explanation

The de Broglie wavelength of an electron in `n^(th)` orbit of Hydrogen atom
`lambda=h/P=h/(mv)`
`rArr lambda=h/((me^2)/(2epsilon_0hn))`
`rArr lambda=((2h^2epsilon_0)/(me^2)) n rArr lambda prop n`
`therefore P to 2`
Magnetic moment of electron in `n^(th)` Bohr orbit
`M="Charge x area "/"Time Period"`
`rArr M=(exxpir^2)/T=(exxpir^2)/((2pi)/omega)=1/2eomegar^2`
`M prop r^2`
`therefore Q to 4`
Magnetic field at centre of hydrogen atom
`B=(mu_0I)/(2r_n)`
`rArr B=(mu_0(e/T_n))/(2r_n)`
`rArr B=(mu_0(e/(2pir_n//v_n)))/(2r_n)`
`rArr B=(mu_0ev_n)/(2pir_n)`
Using `r_n=(epsilon_0 h^2 n^2)/(pi me^2)`
`v_n=e^2/(2epsilon_0hn)`
`rArr B prop 1/n^5`
`therefore R to 1`
Angular momentum of an electron in `n^(th)` orbit of H-atom,
`L=(nh)/(2pi)`
Also `r=(epsilon_0n^2h^2)/(pi me^2)=(4piepsilon_0)/(me^2) L^2`
`L=((me^2)/(4piepsilon_0))^(1/2)xxr^(1/2)`
`rArr L prop r^(1//2)`
`therefore S to 3`