Answer
See answers.
Work Step by Step
The two definitions of the roentgen are:
i. $1.6\times10^{12}$ ion pairs/gram of dry air produced by the radiation
ii. $0.878\times10^{-2}J$ of energy deposited per kg of air.
Start with definition (ii) and relate the two definitions by the value of 35 eV needed to produce an ion pair.
$$1\;R=\frac{0.878\times10^{-2}J}{kg}\frac{1kg}{1000g}\frac{1\;eV}{1.60\times10^{-19}J}\frac{ion\;pair}{35eV}$$
$$1.57\times10^{12}\frac{ion\;pair}{g}$$
The number of ion pairs produced per gram of dry air is about $2\%$ away from that of definition (i), making the two definitions very consistent.