Rescan your photo at 300dpi and make sure you select best quality/no compression
Save your scan. Right click on the properties of the photo and see what it says, it should tell you 300dpi and xxxkb but it will than likely say x.xxMB!
Open your new scan in Irfanfiew
Go to Image> Resize/Resample image
In the LEFT hand column
1. make sure Preserve Aspect ratio is checked
2. Alter the width, usually around 1000 pixels should result in a file under 500kb if scanned at 300dpi
3. press ok
DO NOT USE THE RIGHT hand column to make adjustments... it isn't accurate enough. Thats why we get sooooo many scans that are 10-50kb on here!
Go to file>save as
4. make sure "save quality" slider is right over to good!
5. rename the file
6. click save
now if you right click on the new file, check the new size, if it is around 480KB then that is brilliant!
n.b if the file is still over 500kb or very near, go back and resize the width down a little more and save as a new file again.
I would suggest you start a new thread to ask for a restore of your mums photo
I hope that helps, I know you want a good restore of your mums photo, which is why I'm trying to explain the difference between a good uncompressed scan at 300dpi and poorly compressed resized scan at 300dpi. There is a world of difference.
For examples of a good scan, take a look at the scans Terry Hastie has posted over the last couple of days, they are brilliant and super to work on and do not hurt the eyes.
Terry will now be able to print off all her restores very large and they will still be clear!

Good luck