How to insert random number after text using sed

I'd like to insert a random number after specific text using a shell script. I can generate a random number (32 char):

cat /dev/urandom | tr -dc 'a-z0-9' | fold -w 32 | head -n 1

How do I insert this random number (32_char_random_number) after text (e.g. "alphabet" in a file?:

sed '/\balphabet \b/& 32_char_random_number/' file

thanks.