Red phosphorus is used in the manufacture of safety matches because it is less reactive than other varieties of phosphorus at ordinary temperature.

Option 1: Phosphorescence is the phenomenon of a substance emitting light after absorbing energy. While red phosphorus does not exhibit phosphorescence, it is still used in safety matches for a different reason.

Option 3: Red phosphorus can be converted to white phosphorus on heating. However, this statement is not relevant to the explanation of why red phosphorus is used in the manufacture of safety matches.

Option 4: Red phosphorus does not react with halogens (elements in Group 17 of the periodic table) on heating. While this may be true, it is not the reason why red phosphorus is used in safety matches.

The correct answer is option 2 because red phosphorus is less reactive than other varieties of phosphorus. This lower reactivity makes it safer to handle and reduces the risk of accidental ignition or combustion, making it suitable for use in safety matches.