The rate constant for the forward reaction $\text{A(g)} \rightleftharpoons 2\text{B(g)}$ is $1.5 \times 10^{-3}\,\text{s}^{-1}$ at 100 K. If $10^{-5}$ moles of A and 100 moles of B are present in a 10 litre vessel at equilibrium, then the rate constant for the backward reaction at this temperature is