Relation between Rayleigh and Chi-square random variable

Question

I have read in some of the research papers the following two statements that had created confusion.

1. If $h$ is Rayleigh distributed then $h^2$ is exponential and

2. If $h$ is Rayleigh distributed then $h^2$ is Chi-squared distributed random variable.

Which of these statements are correct.

Also, is it like that if $h$ is Rayleigh distributed with standard deviation as 1 then $h^2$ is Chi-squared distributed.

Any help in this regard will be highly appreciated.