Class 11th

velocity of a freely falling body is v= $\sqrt[]{2gh}$

And $?=\frac{h}{mv}=\frac{h}{m\sqrt[]{2gh}}$

$?=h$ -1

 The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly
a) 1.2 nm (b) 1.2 x 10-3 nm
(c) 1.2 x 10-6  nm (d). 1.2 x 10 nm

(d)

We can write

OS + PS > OP …….(i)

OS > PS – OP …….(ii)

$\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ $>$ $\left|\stackrel{?}{a}\right|$ + $\left|\stackrel{?}{b}\right|$ ….(iii)

The quantity on the LHS is always positive and that on the RHS can be positive or negative. To make both quantities positive, we take modulus of both sides as:

$\left|\left|\stackrel{?}{a}-\stackrel{?}{b}\right|\right|$ > $\left|\left|\stackrel{?}{a}\right|-\mathrm{}\mathrm{}\left|\stackrel{?}{b}\right|\mathrm{}\right|$ ….(iv)

If the two vectors $\stackrel{?}{a}$ and $\stackrel{?}{b}$ act along a straight line but in the opposite direction, then we can write $\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ = $\left|\stackrel{?}{a}\right|$ - $\left|\stackrel{?}{b}\right|\dots ..\left(v\right)$

Combining (iv) and (v), we get

$\left|\stackrel{?}{a}-\stackrel{?}{b}\right|$ $\ge$ $\left|\stackrel{?}{a}\right|$ - $\left|\stackrel{?}{b}\right|$

4.12. No, these cannot be taken as canonical forms because the positions of atoms have been changed. 

4.11. 

Resonance in CO₃^2-, I, II and III represent the three canonical forms.

In these structures, the position of nuclei is the same.

The Lewis dot structure has two single bonds and one double bond.

All three forms have almost equal energy.

The three forms have same number of paired and unpaired electrons; they differ only in their position.

4.10. Bond-length: It is the equilibrium distance between the nuclei of two bonded atoms in a molecule. Bond-lengths are measured by spectroscopic methods.

4.9. Bond strength is directly proportional to the bond order. Greater the bond order more is the bond strength.

4.8. Because of two lone pairs of electrons on O-atom, repulsion on bond pairs is greater in H₂O in comparison to NH₃. Thus, the bond angle is less in H₂O molecules.

4.7