Father keeps asking where my mother is...

I'm sure this has been addressed many times previously, but I just signed up today. So I'll ask. I moved my 85-year-old parents into a personal care facility 4 months ago. My mother needed the extra care, but my father was fine even though he was in the throes of dementia. My mother passed away after 3 weeks in the facility from septic shock. My father has been dealing with her death for the past two months. But this week, something shifted in him and he calls me three times a day after leaving the dining room and returning to his apartment. He wants to know where my mom is. I gently tell him that she passed and we were with her when she passed. He becomes sad and cries, but within 60 seconds, he is back to being present and will often change the subject. I'm not sure what this is, or whether I should continue to tell him about her dying. If I were to say she was out somewhere, he would wait by the door for her to come back to their apartment in the facility. If I say she's in the hospital, he would ask if I could take him to see her. I wouldn't want to give him false hope. How have others handled this? I'm able to immediately change the subject after he asks and cries...and he's fine. But I have to admit, this takes a toll on me as I try to move forward after losing my mom. Thoughts, anyone?