Equal moles of chains of M=1.0x10^5 and of M=1.0x10^3 g mol^-1 are mixed (instead of the pure 1.0x10^5 sample). Compared with the pure sample, the mixture shows

a large fall in M_n (by about half) and a very small fall in M_w (about 1 percent)

a rise in M_n and a fall in M_w

a small fall in M_n and a large fall in M_w

JEE Advanced levelSingle correct optionDifficulty 3 of 3pl162

Equal moles of chains of $M = 1.0 \times 1 0^{5}$ and of $M = 1.0 \times 1 0^{3} g mo l^{- 1}$ are mixed (instead of the pure $1.0 \times 1 0^{5}$ sample). Compared with the pure sample, the mixture shows

Ano change in either average
Ba large fall in $M_{n}$ (by about half) and a very small fall in $M_{w}$ (about 1 percent)
Ca rise in $M_{n}$ and a fall in $M_{w}$
Da small fall in $M_{n}$ and a large fall in $M_{w}$

For the mixture

M_{n} = (1 0^{5} + 1 0^{3}) /2 = 50500

(a fall of about 49.5 percent).

M_{w} = (1 0^{10} + 1 0^{6}) / (1 0^{5} + 1 0^{3}) = 99020

(a fall of about 1 percent). Number averaging responds strongly to many small chains; mass weighting hardly does.