get Lat Lang from a place_id returned by autocomplete place api

The following code snippet which uses Google Places API for android worked for me

Places.GeoDataApi.getPlaceById(mGoogleApiClient, placeId)
    .setResultCallback(new ResultCallback<PlaceBuffer>() {
  @Override
  public void onResult(PlaceBuffer places) {
    if (places.getStatus().isSuccess()) {
      final Place myPlace = places.get(0);
      LatLng queriedLocation = myPlace.getLatLng();
      Log.v("Latitude is", "" + queriedLocation.latitude);
      Log.v("Longitude is", "" + queriedLocation.longitude);
    }
    places.release();
  }
});

Visit Google Places API for Android for a full list of methods to retrieve data from a place