"Nitrogen (gas) is physisorbed over iron (metal) at room temperature": Is this for real?
I think you are misinterpreting the course book issued by your school since it never mentions what happens at room temperature.
For me, none of the books is (seems) wrong, because they do not contradict each other. I will mention each affirmation including the textbook which said it (Levine, or Your book):

Levine says: N2 is physically adsorbed on any solid at low temperature. This agrees with your text saying N2 is physically adsorbed at $\pu{83 K}$ on Fe.
Levine says: N2 is chemisorbed at room temperature on Fe. Your book does not mention about room temperature. No contradiction here.
Your book says N2 is chemisorbed at $\pu{773 K}$. Levine does not mention this temperature, but if it already occurred at room temperature it will also occur at higher.

The only 'gray area' is at which temperature does N2 get chemisorbed (room temperature or not?). In the article of de Boer et al. mentioned by @Linear Christmas above, they measure chemisorption of N2 even at $\pu{23.9 ^\circ C}$.
They clearly state:

Hitherto it has been reported in literature$^{1,2}$ that an iron catalyst starts to chemisorb nitrogen at a measurable rate at about $\pu{200 ^\circ C}$. The chemisorption activity of our intensely reduced sample was considerably higher; already at $\pu{0 ^\circ C}$, nitrogen was chemisorbed at a measurable rate.

Reference:
J. J. F. Scholten, P. Zwietering, J. A. Konvalinka, J. H. de Boer, &quot;Chemisorption of nitrogen on iron catalysts in connection with ammonia synthesis. Part 1.—The kinetics of the adsorption and desorption of nitrogen,&quot; Trans. Faraday Soc. 1959, 55, 2166-2179 (https://doi.org/10.1039/TF9595502166).