Question

6. Wavelength associated with a water molecule moving with a velocity of 500 ms' is
(a) 44.3 pm
(b) 443 pm
(e) 0,0443 pm
7. Select the correct statement(s).
(d) 0.4​

Answer 1

Answer : The correct option is, (a) 44.3 pm

Explanation :

According to de-Broglie, the expression for wavelength is,

$\lambda=\frac{h}{p}$

and,

$p=mv$

where,  

p = momentum, m = mass, v = velocity

So, the formula will be:

$\lambda=\frac{h}{mv}$

where,

h = Planck's constant = $6.626\times 10^{-34}Js$

$\lambda$ = wavelength

m = mass

v = velocity = 500 m/s

First we have to calculate the mass of water molecule.

As, mass of 1 mole or $6.022\times 10^{23}$ molecules of water = 18 g

So, mass of 1 molecules of water = $\frac{18}{6.022\times 10^{23}}g=\frac{0.018}{6.022\times 10^{23}}kg$

Now we have to calculate the wavelength.

Now put all the given values in the above formula, we get:

$\lambda=\frac{h}{mv}$

$\lambda=\frac{6.626\times 10^{-34}Js}{(\frac{0.018}{6.022\times 10^{23}}kg)\times (500m/s)}$

$\lambda=4.43\times 10^{-11}m=44.3pm$

conversion used : $1m=10^{-12}pm$

Therefore, the wavelength of water molecule is 44.3 pm