A B737-700 STAB TRIM MOTOR FAILED AT THE START OF THE ARRIVAL DSCNT. AN EMER WAS DECLARED AND THE FLT DIVERTED TO A NEARBY ARPT WITH A LONG RWY.

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ON FLT ZZZ1-ZZZ2; WE INITIATED OUR DSCNT INTO ZZZ2. UPON VACATING OUR CRUISE ALT; THE 'STABILIZER OUT OF TRIM' LIGHT ILLUMINATED. WE HAD NOTED A REPEAT WRITE-UP ON THIS LIGHT PRIOR TO OUR DEP FROM ZZZ1. WE COMPLETED THE 'STABILIZER OUT OF TRIM' QRH CHKLIST. AFTER DISCONNECTING THE 'B' AUTOPLT; PER THE QRH; WE DISCOVERED NEITHER PLT'S CTL YOKE ELECTRIC TRIM SWITCHES OPERATED. FROM THIS CONCLUSION; THE QRH DIRECTED US TO THE 'STABILIZER TRIM INOP' QRH CHKLIST. WE CONFIRMED THAT THE MANUAL TRIM OPERATED NORMALLY AND THAT NO CIRCUIT BREAKERS WERE POPPED. MAINT CTL AND DISPATCH WERE CONTACTED OVER THE RADIO AND ADVISED OF OUR MALFUNCTION AND THE CHKLISTS BEING RUN. AT THIS TIME WE ELECTED A ZZZ DIVERSION DUE TO THE FLAPS 15 DEG LNDG. DISPATCH SENT US NON-NORMAL LNDG DATA VIA ACARS. THE CAPT DECLARED AN EMER WITH APCH AND REQUESTED A LONG FINAL. THE CAPT ADVISED THE CABIN CREW THAT OUR ELECTRIC TRIM WAS NOT OPERATING; BUT OUR MANUAL TRIM SYS WORKED NORMALLY. HE INFORMED THEM OF OUR DECISION TO DIVERT TO ZZZ FOR THE LONGER RWY AND APCH SEGMENT. HE TOLD THE FLT ATTENDANTS WE WOULD BE LNDG IN 20-25 MINS AND THE LNDG ITSELF WOULD BE NORMAL WITH NO SPECIAL INSTRUCTIONS NECESSARY. FOLLOWING THIS BRIEF; HE GAVE A PA TO THE PAX INFORMING THEM OF OUR DECISION TO GO TO ZZZ AND THAT A PORTION OF OUR TRIM SYS WAS NOT OPERATING PROPERLY; BUT THAT OUR MANUAL TRIM SYS OPERATED NORMALLY. WE HAD AN UNEVENTFUL FLAPS 15 DEG APCH AND LNDG. WE WERE PROVIDED WITH A LONG FINAL AND AMPLE TIME TO CONFIGURE EARLY PER THE CHKLIST. THE LNDG WAS NORMAL WITH NO UNUSUAL ATTITUDES OR DSCNT RATES. UPON EXITING; TWR QUERIED US AS TO WHETHER WE NEEDED FURTHER ASSISTANCE. WE INFORMED THEM WE DID NOT; AND TAXIED TO THE GATE AND DEPLANED. AFTER THE PAX DEPLANED; THE CAPT GAVE THE FLT ATTENDANTS A DEBRIEF AND WAS TOLD THAT THERE HAD NOT BEEN ANY ADVERSE PAX REACTION TO THE DIVERSION. THE CAPT THEN PHONED SCHEDULING FOLLOWING A CALL TO THE OPS DUTY OFFICER TO DETERMINE WHAT WAS PLANNED FOR THE FOLLOWING DAY. SCHEDULING ASKED IF WE WERE WILLING TO WAIVE OUR 8 HRS TO FLY TO ZZZ2. THE DUTY DAY WAS SCHEDULED AT 12 HRS 18 MINS WITH 7 HRS 32 BLOCK TIME. WHEN WE ARRIVED AT THE GATE; WE HAD FLOWN 8 HRS 11 MINS AND HAD BEEN ON DUTY; LESS RELEASE TIME OF 12 HRS 34 MINS. ADDING CHK-IN TIMES; I HAD BEEN ON DUTY FOR 6 MINS SHY OF 14 HRS. WE DECIDED WE WERE DONE IN ZZZ.