In the given TLC, the distance of spot $ A $ and $ B $ are 5 cm and 7 cm, from the bottom of the TLC plate, respectively. The $ R_f $ value of $ B $ is $ x \times 10^{-1} $ times more than $ A $. The value of $ x $ is _________ .

Question

The half-life of $^{65}$Zn is 245 days. After $x$ days, 75% of the original activity remained. The value of $x$ in days is __________ (Nearest integer).}
(Given: $\log 3 = 0.4771$ and $\log 2 = 0.3010$)

Answer 1

The retention factor ($ R_f $) is defined as the ratio of the distance a compound travels to the distance the solvent front travels. The solvent front advanced 10 cm. $ R_f $ values for spots $ A $ and $ B $ are calculated as follows:

$ R_{fA} = \frac{5\, \text{cm}}{10\, \text{cm}} = 0.5 $

$ R_{fB} = \frac{7\, \text{cm}}{10\, \text{cm}} = 0.7 $

Given that $ R_{fB} $ is $ x \times 10^{-1} $ times greater than $ R_{fA} $:

$ 0.7 = x \times 10^{-1} \times 0.5 $

Solving for $ x $:
$ 0.7 = \frac{x}{10} \times 0.5 $
$ x = \frac{0.7 \times 10}{0.5} = 14 $

The value of $ x $ is 14, which is within the specified range of 15,15.

In the given TLC, the distance of spot \( A \) and \( B \) are 5 cm and 7 cm, from the bottom of the TLC plate, respectively. The \( R_f \) value of \( B \) is \( x \times 10^{-1} \) times more than \( A \). The value of \( x \) is _________ .

Correct Answer: 15

Solution and Explanation

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