An employee of the state who has accumulated six hundred hours of unused sick leave shall be entitled to be paid for additional unused sick leave at a rate equal to fifty percent of his hourly wage multiplied by the number of hours of unused sick leave over six hundred hours, not to exceed one hundred twenty hours of such sick leave in any one fiscal year. Payment for sick leave as authorized by this section shall be paid only on either the payday immediately following the first full pay period in January or the first full pay period in July. An eligible employee shall notify his agency of his desired payment date and the number of unused sick leave hours he wishes to convert pursuant to this section before payment can be authorized.