Household utility function

Hi everyone
Excuse me for this low level question. I am a beginner. My question is about the household utility function. I have seen several types of household utility functions: One of the functions is as follows:

Here n is the labor.
Is this utility function correct?
thank you

What do you mean with correct? It satisfies the usual assumptions like increasing in consumption, decreasing in hours works, and risk aversion. The infinite Frisch elasticity due to linear labor is a bit harder to swallow but not uncommon.